22 girls and 11 boys are divided into groups for a project. The same number of girls and the same number of boys are put in each group. What is the greatest number of groups that can be made?
Answer:
11
Step-by-step explanation:
find ratio of girls to boys
22:11 divide by 11
2:1
2girls and 1boy in every boy makes 11 groups
please help
after putting the first 2 terms together and the second 2 terms together, what needs to be in the middle
1. an equal sign
2. a plus sign
3. perenthatesis around all 4 terms
4. nothing
After putting the first 2 terms together and the second 2 terms together, what needs to be in the middle is; Parenthesis around all 4 terms
How to factor Algebraic Expressions by grouping?Factorization by grouping in algebra simply means that we need to group the terms with common factors before factoring.
Now, some of the steps to take in this regards are;
- From the groups of the given expression a factor can be taken out from each group.
- Factorize each group
- Now take out the factor common to group formed.
Thus, from the above after grouping the terms together, the next thing to be in the middle is to put parentheses around the 4 terms.
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What is the length of the dotted line in the diagram below? Round to the nearest tenth.
The lenght of the dotted line in the given diagram is 5.92
The dotted line in the given diagram is the diagonal of the rectangle. The lenght of diagonal can be calculted using phytagoras theorem:
diagonal² = length² + wide²
From the diagram, we know that the wide of the rectangle is 1, however we have no information about the length of the rectangle yet. If we look to the attached triangle, we can know that the lengt of rectangle is actually the hypotenuse of the triangle.
We can find the hypotenuse of the triangle using the phytagoras theorem:
hypotenuse² = base² + height²
hypotenuse² = 3² + 5²
hypotenuse² = 9 + 25
hypotenuse² = 34
We can use the value of squred hypotenuse as the squared length to find the length of the diagonal:
diagonal² = length² + wide²
diagonal² = hypotenuse² + wide²
diagonal² = 34 + (1)²
diagonal² = 35
diagonal = 5.92
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Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.
Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions.
Write two expressions for this situation, one representing the cost per customer and the other representing the average number of customers. Assume that x represents the number of $1 increases in the cost of the buffet.
Enter the correct answer in the box. Type the cost expression on the first line and the customer expression on the second line.
The two expressions for this situation, with one representing the cost per customer and the other representing the average number of customers are:
Cost: 10 + x
Customer: 16 - 2x
Inequality: 160 - 4x - 2x² ≥ 130.
How to write two expressions that models this situation?Based on the information provided, we can logically deduce that the amount of money being charged by Noah per buffet is equal to $10. Also, the total number of customers that chose buffet every hour is equal to 16 customers.
For an increase in the cost of buffet by $1, the average number of customers who selected the buffet would decrease by 2 per hour and the minimum revenue per hour is $130.
Therefore, an expression that represents the cost per customer is given by;
Cost: 10 + x
Additionally, an expression that represents the average number of customers;
Customer: 16 - 2x
Lastly, an inequality that would help Noah make the best pricing decisions is as follows;
Revenue = Cost × Customers
(10 + x) × (16 - 2x) ≥ 130
160 - 20x + 16·x - 2x² ≥ 130
160 - 4x - 2x² ≥ 130
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or At the end of the year, cars made in the current year are marked down to make room for next year's models. One particular model has a sale price of $13,065, which is 25% less than it sold for when it was new. What was the original price of the vehicle?
The original price of the car is $17420
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Given that, a sale price of $13,065, which is 25% less than it sold for when it was new,
We need to find the original price of the vehicle,
Let the original price be x,
x - 25% of x = 13065
x(1-25%) = 13065
x(75/100) = 13065
x = 13065 × 100 / 75
x = 100 × 174.2
x = 17420
Hence, the original price of the car is $17420
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0=(2x-3)(x+1)? Answer or how to solve
Answer:
x = 3/2 or x = -1
Step-by-step explanation:
Holly bought a magazine subscription for 8 months. She paid $28. Holly wanted to find the price, p, of the subscription each month. She created the model shown to find the price
Therefore , the solution of the given problem of unitary method comes out to be $3.5 is the average price.
What exactly is a unitary method?After calculating the size of a small slice, multiply the quantity by two to complete a task using the unitary technique. Simply expression, the unit variable technique works to separate a coded item from a certain group or collection of groups. For instance, 40 pens would cost Rs. 400 (or 400 pounds, $1.01). It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality.
Here,
Given :
subscription for 8 months
She paid $28 and Holly wanted to find the price, p
Price for one month is :
=> 28/8
=> $3.5
Therefore , the solution of the given problem of unitary method comes out to be $3.5 is the average price.
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The complete question is "Holly bought a magazine subscription for a year. She paid $27. Holly wanted to find the price, p, of the subscription each month. She created the model shown to help find this price. 27 р |р |р |р |р |р |р |р | Р | Р |р | p What was the price of the subscription each month? F $39.00 G $2.25 H $324.00 3 $22.50"
A school supply company is giving away free chalkboards to promote their dust-free chalk. The company can spend up to $3,293 on the chalkboards. If each chalkboard costs the company $37, how many chalkboards will they be able to give away?
The number of chalkboards that the school will be able to give away is 89.
How many chalkboards will the school give away?In order to determine how many chalkboards the school can give away, the mathematical operation that would be used is division.
Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.
Number of chalkboards the school can give away = total amount the school has to spend / cost of each chalkboard #
$3,293 / $37 = 89
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Tina is taking her husband and three kids to the movies everyone gets a soda for two hours and $2.50 and a popcorn for $3.50 are two different expressions that will allow Tina to calculate the total cost of the soda and popcorn
Total cost of soda and popcorn for 5 people = $6.00 x 5 = $30.00
How can we prove it ?Yes, two different expressions to calculate the total cost of the soda and popcorn for Tina and her family are:
Expression 1: Total cost of soda = $2.50 x 5 (5 people) = $12.50
Total cost of popcorn = $3.50 x 5 = $17.50
Total cost of soda and popcorn = $12.50 + $17.50 = $30.00
Expression 2: Total cost of soda and popcorn for one person = $2.50 + $3.50 = $6.00
Total cost of soda and popcorn for 5 people = $6.00 x 5 = $30.00
What is ratio ?A ratio is a comparison of two or more values. It is a way of expressing the relationship between two or more quantities in the form of a fraction. The numerator of the fraction represents the first quantity and the denominator represents the second quantity. The ratio can be written in the form of a:b, where a and b are the two quantities being compared.
For example, if you have 4 apples and 2 bananas, the ratio of apples to bananas can be expressed as 4:2 or 2:1. This means that for every 2 bananas, there are 4 apples. Ratios can also be used to compare values of different units, for example, miles to kilometers or pounds to kilograms.
Ratios are widely used in many fields, including finance, cooking, construction, and physics, to compare and express the relationship between different quantities. They provide a simple and intuitive way to compare values and help to make sense of complex data.
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Find the missing number of the unit rate 36/3=\1
12 is the missing number of the unit rate 36/3=\1.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let us consider the missing number be x in the given equation
36/3=x/1
36 and 3 are the multiples of 3 so divide numerator and denominator by 3
36 divided by 3 is equal to twelve
so the value of x is 12
Hence, 12 is the missing number of the unit rate 36/3=\1.
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Enrique and Taylor are 280 feet apart when they start walking toward one another. Taylor walks twice as fast as Enrique, so whenever Enrique travels & feet, Taylor travels 2x feet. Let a represent the number of feet Enrique has traveled since he started walking toward Taylor.(A) Write an expression in terms of a to represent the total number of feet Enrique and Taylor have walked toward one another.(B) Write an expression in terms of a to represent the distance (in feet) between Enrique and Taylor.(C) Let & represent the distance (in feet) between Enrique and Taylor. Write a formula that expresses d in terms of ..
They begin at a distance of 210 feet, hence the distance between them is equal to 210 - 2sx feet
A) Accordingly, if x equals "the number of feet Alan has gone since he started walking toward Victoria," then A) the combined distance (in feet) covered by the two walkers must be 2x, and B) Alan's distance from Victoria must be 210 - 2x.
B) In other words, if Alan and Victoria are walking at the same speed, let's call that speed s, then the total distance each of them has traveled is equal to sx ft (x = the amount of time since they began walking), which equals 2sx ft.
C) They begin at a distance of 210 feet, hence the distance between them is equal to 210 - 2sx feet.
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what is the answer? (brainliest) if someone helped!
1) Completing the square is a good solving option when b is an even number.
2) The discriminant of the quadratic equation y² = x² + 4x + 4 is positive.
What is discriminant?
The discriminant of a polynomial is a number that depends on the coefficients and allows some properties of the roots to be deduced without having to compute them.
1) Completing the square is a good solving option when b is an even number.
Completing the square is a technique used to solve quadratic equations of the form ax² + bx + c = 0 by rewriting the equation as a perfect square. This technique is particularly useful when b is an even number because it makes it easier to recognize the perfect square pattern.
For example, if b = 2, then the equation can be written as ax² + 2x + c = 0. By adding and subtracting the same term, this equation can be rewritten as a(x + 1)² + (c - a) = 0, which is a perfect square. Solving the equation then becomes a matter of finding the square root of the constant term.
If b is an odd number, the equation can still be solved using the completing the square technique, but it may require more steps.
Hence, Completing the square is a good solving option when b is an even number.
2) The discriminant of a quadratic equation of the form ax² + bx + c = 0 is given by b² - 4ac. In this case, a = 1, b = 4, and c = 4, so the discriminant is b² - 4ac = 4² - 4 * 1 * 4 = 16 - 16 = 0.
A positive discriminant means that the equation has two real and distinct roots, a negative discriminant means that the equation has two complex roots, and a zero discriminant means that the equation has one real root (a double root).
Hence, The discriminant of the quadratic equation y² = x² + 4x + 4 is positive.
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A robot uses a range sensor that can measure ranges from Om and 3m. For simplicity, assume that actual ranges are distributed uniformly in this in- terval. Unfortunately, the sensor can be faulty. When the sensor is faulty, it constantly outputs a range below lm, regardless of the actual range in the sensor's measurement cone. We know that the prior probability for a sensor to be faulty is p=0.01. Suppose the robot queried its sensor N times, and every single time the measurement value is below lm. What is the posterior probability of a sensor fault, for N = 1, 2, ..., 10. Formulate the corresponding proba- bilistic model.
The posterior probability of a sensor fault increases as the number of consecutive measurements below 1m increases.
Let P(F) be the prior probability of a sensor fault and P(M|F) be the probability of measurements below 1m given a faulty sensor. Then, the posterior probability of a sensor fault given N consecutive measurements below 1m is given by
P(F|M1 ,M2 ,...,MN )=P(F)P(M1|F)P(M2|F)....P(MN |F)/P(M1 ,M2 ,...,MN )
P(M1 ,M2 ,...,MN ) = P(M1)P(M2)....P(MN) = (1/3)^N
Therefore,
P(F|M1 ,M2 ,...,MN )=P(F)(1/3)^N
For N = 1,2,...,10
P(F|M1 ,M2 ,...,MN ) = 0.01 (1/3)^N
For N = 1, P(F|M1)= 0.01/3
For N = 2, P(F|M1,M2)= 0.01/9
For N = 3, P(F|M1,M2,M3) = 0.01/27
Similarly, for N= 4,5,6,7,8,9,10
P(F|M1,M2,M3,M4,M5,M6,M7,M8,M9,M10) = 0.01/81, 0.01/243, 0.01/729, 0.01/2187, 0.01/6561, 0.01/19683, 0.01/59049 respectively.
The posterior probability of a sensor fault increases as the number of consecutive measurements below 1m increases.
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Can someone help me please I don’t get this
[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{\textit{we'll be using this one}}{log_a a^x = x}\qquad \qquad a^{log_a x}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 140\\ P=\textit{original amount deposited}\dotfill & \$70\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &5 \end{cases}[/tex]
[tex]140 = 70e^{\frac{r}{100}\cdot 5} \implies \cfrac{140}{70}=e^{\frac{r}{20}}\implies 2=e^{\frac{r}{20}}\implies \log_e(2)=\log_e\left( e^{\frac{r}{20}} \right) \\\\\\ \log_e(2)=\cfrac{r}{20}\implies \ln(2)=\cfrac{r}{20}\implies 20\ln(2)=r\implies \boxed{13.86\approx r}[/tex]
Deb is searching online for airline tickets. Two weeks ago, the cost to fly from Hartford to Boston was $225. Now the cost is $300. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Answer:
The percent increase for airfares from Hartford to Boston is:
(300 - 225)/225 * 100% = 33.333%
If the airline charges an additional $50 baggage fee with the new ticket price, the percent increase from 300 to 350 is:
(350 - 300)/300 *100% = 16.67%
Madison has this equation. Find the y-value when x = -3.
*
[tex]y=0.5x^{2} +4[/tex]
Based on Madison's equation, the y-value is equal to 8.5.
How to find the y-value?In Mathematics, a function is typically used for uniquely mapping an independent value (input variable or domain) to a dependent value (range or output variable).
In order to use the given function to determine the value of y (y-value), we would have to substitute the values of x (x-value or domain) into the function and then evaluate as follows;
y = 0.5x² + 4
y = 0.5(-3)² + 4
y = 0.5(9) + 4
y = 4.5 + 4
y = 8.5.
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likes to collect records. Last year had 10 records in collection. Now has 14 records. What is the percent increase of collection?
The percent increase in the collections is 40%.
What is the percent increase?Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign that is used to represent percentage is %.
Percent increase = (increase in the number of collections / initial collections) x 100
Increase in collections = 14 - 10 = 4
= (4/10) x 100 = 40%
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Determine the area of each composite figure. Round to the nearest tenth if necessary.
The solution is, the area of the given figure is 38.6 ft^2.
What is area of trapezoid?The area of a trapezoid is found using the formula, A = ½ (a + b) h,
where 'a' and 'b' are the bases (parallel sides) and 'h' is the height .
here, we have,
from the given figure , we get,
the trapezoid's,
parallel sides are, 9 ft. & 7ft.
height = 3.6 ft.
so, area = ½ (a + b) h,
i.e. A = 28.8 ft^2
Again, area of the triangle is,
area = 1/2 * base * height
= 1/2 * 7* 2.8
= 9.8
total area = 38.6 ft^2
Hence, The solution is, the area of the given figure is 38.6 ft^2.
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Compare using<>=
1/3×5/7 ⭕️ 2/5+4/4
The comparison is
1/3×5/7 < 2/5+4/4
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
1/3×5/7 ⭕️ 2/5+4/4
we solve the quantities one by one
1/3×5/7
= 5/ 21
and, 2/5+4/4
= 28/20
= 7/5
So, 1/3×5/7 ⭕️ 2/5+4/4
5/21 ⭕️ 7/5
25/105 < 174/105.
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5. 315+x=285 -86+20=R+20 d) inte zero. By how many degrees did the temperature drop? The temperature in Kiev was 10 °C below zero. Then it dropped to 24 °C beloy Divis 6. A fish was swimming at 52 m below sea level. It then swam down to 120 m below sea level. How many metres downwards did the fish swim? 7. What us the difference between the elevation of the Dead Sea (-420 m) and Lake Assal (-156 m)? What is the sum of the following temeratures? -10°C: 24 °C -12 °C 8 °C -1 °C ers: ultiplying and dividing integers mis section, you will revise multiplication and division of integers. nt down in intervals of 5 to see happens when you multiply Now start with a negative integer and count up in intervals of 5 as you multiply:
5. The temperature dropped by 10 - (-24) = 34 degrees.
6. The fish swam down 120 - 52 = 68 meters.
7. The difference between the elevation of the Dead Sea and Lake Assal is (-420) - (-156) = 264 meters.
8. The sum of the temperatures is -10 + 24 - 12 + 8 - 1 = 9 degrees Celsius
What is a temperature drop?A temperature drop refers to a decrease in the temperature from one point to another, for example, from a higher temperature to a lower temperature.
It could then be concluded that the correct answers are 34 degrees, 68 meters, 264 meters, and 9 degrees Celsius respectively.
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Identify each of the following as examples of (1) attribute (qualitative) or (2) numerical (quantitative) variables: a. The breaking strength of a given type of string. b. The hair color of children auditioning for the musical Annie. c. The number of stop signs in towns of fewer than 500 people. d. Whether or not a faucet is defective. e. The number of questions answered correctly on a standardized test. f. The length of time required to answer a telephone call at a certain real estate office
The number of questions answered correctly on a standardized test and the length of time required to answer a telephone call at a certain real estate office are all numerical (quantitative) variables.
a. The breaking strength of a given type of string. Numerical (quantitative)
b. The hair color of children auditioning for the musical Annie. Attribute (qualitative)
c. The number of stop signs in towns of fewer than 500 people. Numerical (quantitative)
d. Whether or not a faucet is defective. Attribute (qualitative)
e. The number of questions answered correctly on a standardized test. Numerical (quantitative)
f. The length of time required to answer a telephone call at a certain real estate office. Numerical (quantitative)
For example, if a standardized test had 10 questions, and a student answered 7 correctly, the numerical (quantitative) variable for the number of questions answered correctly would be calculated with the formula: 7/10 = 0.7 or 70%. The length of time required to answer a telephone call at a certain real estate office can also be calculated numerically (quantitatively) by taking the total time of the call and dividing it by the number of calls. For instance, if the total time of 10 telephone calls was 80 minutes, the numerical (quantitative) variable for the length of time required to answer a telephone call would be calculated with the formula: 80/10 = 8 minutes.
Based on the examples given, the breaking strength of a given type of string, the number of stop signs in towns of fewer than 500 people, the number of questions answered correctly on a standardized test and the length of time required to answer a telephone call at a certain real estate office are all numerical (quantitative) variables, while the hair color of children auditioning for the musical Annie and whether or not a faucet is defective are attribute (qualitative) variables.
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What is the effect on the graph of f(x)=x^2 when it is transformed to h(x)=3x^2-7?
The transformation h(x)=3x^2-7 will cause the graph of f(x)=x^2 to stretch vertically by a factor of 3 and shift 7 units downward.
Hwo to determine the effect of the transformationFrom the question, we have the following parameters that can be used in our computation:
f(x) = x^2
h(x) = 3x^2 - 7
This means that
h(x) = 3f(x) - 7
This in other words, the transformation "stretches" the graph of f(x) = x^2 vertically by a factor of 3 and "translates" it vertically by shifting it downward by 7 units.
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Find the minimum value of the function f(x) = x² +10.5x + 20 to the nearest
hundredth.
well, the quadratic function is simply a parabola that looks like a bowl with a "minimum" at its vertex, so
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+10.5}x\stackrel{\stackrel{c}{\downarrow }}{+20} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{10.5}{2(1)}~~,~~20-\cfrac{10.5^2}{4(1)} \right)\implies \left( -\cfrac{10.5}{2}~~,~~20-\cfrac{110.25}{4} \right) \\\\\\ \left( -5.25~~,~~20-27.5625 \right) ~~ \approx ~~ \boxed{(-5.25~~,~-7.56)}[/tex]
Nate sells wooden boxes. He sells 8 small boxes and 3 large boxes. He sells small boxes for $12 each. He sells large boxes for $17 each. What is the most reasonable estimate of the total sale of the wooden boxes?
The most reasonable estimate of the total sale of the wooden boxes would be= $147
How to calculate the total sale of the wooden boxes?The total number of small wooden boxes= 8
The price for the small boxes= $12.
The total price for the small boxes= 12×8 = $96
The total number of larger wooden boxes= 3
The price for the larger boxes= $17
The total price for the larger boxes= 17×3 = $51
The total price for all the boxes = 96+51 =$147
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A soccer player has a large cylindrical water cooler that measures 3 feet in diameter and is 4 feet tall. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water are in the water cooler when it is completely full? Use π = 3.14 and round to the nearest hundredth. 28.26 gallons 113.04 gallons 211.38 gallons 845.54 gallons
The volume of the cylindrical water cooler is 211.38 gallons. Therefore, option C is the correct answer.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, a soccer player has a large cylindrical water cooler that measures 3 feet in diameter and is 4 feet tall.
Now, radius = 3/2 =1.5 feet
We know that, the formula to find the volume of a cylinder is πr²h.
Here, 3.14×1.5²×4
= 28.26 cubic feet
In gallons = 28.26×7.48
= 211.38 gallons
Therefore, option C is the correct answer.
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The correct option is C, 211.38. Hope this helps :)
Recall that a bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. The mean time during peak business hours under the current system is roughly 9 to 10 minutes. The bank manager hopes that the new system will have a mean waiting time that is less than six minutes. The mean of the sample of 100 bank customer waiting times in Table 1.8 is 5.46. If we let u denote the mean of all possible bank customer waiting times using the new system and assume that the standard deviation equals 2.47:
(a) Calculate 95 percent and 99 percent confidence intervals for u.
(b) Using the 95 percent confidence interval, can the bank manager be 95 percent confident that u is less than six minutes? Explain.
(c) Using the 99 percent confidence interval, can the bank manager be 99 percent confident that u is less than six minutes? Explain.
(d) Based on your answers to parts b and c, how convinced are you that the new mean waiting time is less than six minutes?
z is the z-score for the desired confidence level. For 95 percent confidence, z = 1.96 and for 99 percent confidence, z = 2.58.
(a) To calculate the 95 percent and 99 percent confidence intervals for u, we can use the formula:
mean ± z*(standard deviation/sqrt(sample size))
Plugging in the values, we get:
95 percent confidence interval: 5.46 ± 1.96*(2.47/sqrt(100)) = 5.46 ± 0.39
99 percent confidence interval: 5.46 ± 2.58*(2.47/sqrt(100)) = 5.46 ± 0.52
(b) For the 95 percent confidence interval, the interval is 5.46 ± 0.39, which means that we can be 95 percent confident that the true mean waiting time u is between 5.07 and 5.85 minutes. Since 6 minutes falls outside this interval, we cannot be 95 percent confident that u is less than 6 minutes.
(c) For the 99 percent confidence interval, the interval is 5.46 ± 0.52, which means that we can be 99 percent confident that the true mean waiting time u is between 4.94 and 5.98 minutes. Since 6 minutes falls outside this interval, we cannot be 99 percent confident that u is less than 6 minutes.
(d) Based on the results of the 95 percent and 99 percent confidence intervals, we can conclude that there is not enough evidence to be confident that the new mean waiting time is less than six minutes.
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(50 POINTS AND BRAINLYEST)
Please answer both in the image below
[(x₁ + x₂)/2, (x₁ + x₂)/2] is the formula to find: B. the midpoint.
[(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)] is the formula to find: A. the point that partitions a segment into a ratio of m : n, where m : n is not 1 : 1.
What is the midpoint theorem?In Mathematics, the midpoint theorem states that in a triangle, the line segment which joins the midpoints of any two (2) sides of the triangle must be parallel to the third side and congruent to half of the length of the third side.
What is a line ratio?In Mathematics, a line ratio can be defined as the set of points that partitions a line segment into a ratio of m : n and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
where:
m : n is not 1 : 1.
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help please
answer 13 only
The required expected value of the pointer landing on the blue is 9.4 times.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
here,
From the table,
Frequency of blue color = 14
Total outcome = 75
Probability of landing on blue = P(b) = 14 / 75
Now,
The spinner is spun 50 times,
The expected value of the color blue is given as,
E(b) = n × P(b)
E(b) = 50 × 14/75
E(b) = 9.4 times
Thus, the required expected value of the pointer landing on the blue is 9.4 times.
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Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
4 is multiplied by the difference of 5 and a number.
The solution is, the expression is => 4*(5-x)
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
let, the number is x.
now, when,
4 is multiplied by the difference of 5 and a number.
so, we get,
the expression is => 4*(5-x)
Hence, The solution is, the expression is => 4*(5-x)
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Give an example of a function f where 0 is in the domain of f,but limx→0 f (x)is undefined.
An example of a function f where 0 is in the domain of f, but limx→0 f(x) is undefined is the piecewise function:
f(x) = x + 45 if x < 0
f(x) = x + 33 if x ≥ 0.
What function has 0 on its domain, such that the limit there is undefined?Remember how the limit works. It only exist if the approach from left and right give the same value.
Then we can define a piecewise function like:
f(x) = x + 45 if x < 0
f(x) = x + 33 if x ≥ 0.
Clearly, 0 belongs to the domain, and the limits are:
[tex]\lim_{x \to 0_-} f(x) = 45\\\\\lim_{x \to 0_+} f(x) = 33[/tex]
These limits are different, thus the limit when x tends to zero is undefined.
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