Answer:
70x+44y
Step-by-step explanation:
step 1: distribute
84x+82y−(14x+38y)
84x+82y−14x−38y
step 2: combine like terms
84x+82y−14x−38y
84+82−14−38
70x+44y
Sally is near the end of a three year lease on a car with an original msrp of $38,000. her leasing company claims that the car is now worth only $28,500. which percentage represents the residual value of sally’s leased car? a. 25% b. 33% c. 67% d. 75% please select the best answer from the choices provided a b c d
The right answer is D.
Detailed explanation:
$35,000. Original cost of the vehicle
The car's current value is $28,500.
The residual worth of Sally's leased vehicle is equal to x.
Current Price x * 38,000 = 28,500 x = 28,500/38,000 x = 0.75 Residual value * Original Price
Since we must determine the proportion
Divide the residual value by 100, or 0.75 * 100, to get 75%.
The right answer is D.
What exactly does leasing mean?A lease is a contract in which the owner of an asset (the lessor) agrees to let the lessee use it in exchange for a specific amount of money (the rent), which may or may not be based on any factors, for a specified amount of time (the lease term), which may or may not be flexible.
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Write the linear equation for the graph of line q.
y = x+
I need help now please
Answer:8,5
Step-by-step explanation: look at where the dots are and see the numbers
Answer:
AC = 3[tex]\sqrt{5}[/tex] ≈ 6.71
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
AC² = AB² + BC² = 6² + 3² = 36 + 9 = 45 ( take square root of both sides )
AC = [tex]\sqrt{45}[/tex] = [tex]\sqrt{9(5)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex] = 3[tex]\sqrt{5}[/tex] ← exact value
AC ≈ 6.71 ( to the nearest hundredth )
What is the 75th term of the arithmetic sequence?
-1113, -1094, -1075, -1056, -1037, ...
Enter your answer in the box.
Answer:
1183
Step-by-step explanation:
75th term of Arithmetic sequence is 1183 Given: -1, 15, 31,... is Arithmetic series To find: The 75th term of the arithmetic sequence -1, 15, 31
Between which two numbers will you find in 5.634x10 to the 2 power
The number 5.634x10 to the 2nd power can be expressed as 563.4. The numbers between which 563.4 falls are 560 and 567.
a vertical asymptote is a vertical line that the graph of the function approaches as x tends to positive or negative infinity. b. a vertical asymptote is a vertical line x
A vertical asymptote basically means of a graph on a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.
In a graph a vertical asymptote is a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a. And similarly the horizontal asymptote in a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞.
At x = a in a graph where a is a zero for a factor in the denominator the removable discontinuity occur that is common with a factor in the numerator.
Factor the numerator and denominator.
It is set it equal to zero and solve if any factors are common to both the numerator and denominator.
This is removable discontinuity type location.
In mathematics a graph is defined as a diagrametical or a pictorial representation that helps to represents data or values in an organized manner. The points that are shown on the graph are use to mark of represent the various value or relation between two value .
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lake erie line graph text-based description: line graph showing declining snowfall totals with distance from the shore of lake erie. the gradual decline from around 425 cm to 375 cm between 0 and 30 km increases with total snowfall at 250 cm by 50 km. there is little decline in the following 10 km but it does drop again by around 50 cm over the next 10 km. the remaining decline is relatively consistent out to 100km, with snowfall there at 150 cm. what is the spatial scale at which the data was collected?
The spatial scale at which the data was collected is the distance from the shore of Lake Erie.
We can see that the data shows a gradual decline in snowfall totals with increasing distance from the shore of Lake Erie. The decline starts at around 425 cm at 0 km and decreases to 375 cm by 30 km. It then decreases more quickly over the next 20 km before declining relatively consistently out to 100 km, where the snowfall is 150 cm.
The graph shows the declining snowfall totals with increasing distance from the shore of Lake Erie, starting from 0 km and ending at 100 km. The data points are measured in increments of 10 km, with the total snowfall measured in cm.
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The variable whose effect on the response variable is to be assessed by the experimenter is called
The factor is the variable that the experimenter will use to judge its impact on the response variable.
A dependent variable is one that is altered as a result of the modification of an independent variable. The outcome you're trying to measure "depends" on your independent variable. Response variables in statistics are another name for dependent variables (they respond to a change in another variable).
The terms are the numbers or the variables added together, factors are the numbers or the variables that are multiplied together and the coefficient is the number multiplied to the variable.The coefficient of a variable term is that word's numerical factor.
A factor is a type of statistical data that is used to hold categorical variables. Categorical variables can be categorised into only a few groups. Continuous variables, on the other hand, are infinitely variable.The variable being measured or tested in an experiment is known as the dependent variable.
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for that, she needs 20 grams of a 52% solution of salt. she has two bottles of salt water. one bottle contains a 40% salt solution and the other a 70% salt solution. how much of each must she use to make the solution she needs?
The solution used to make 40% of salt solution is 12 grams and 70% of salt solution is 8 grams.
Let us consider 'a' represents the 40% of salt in water.
And 'b' represents the 70% of salt in water.
Total salt required to make 52% salt solution = 20 grams
Required equations is :
a + b = 20
⇒ a = 20 - b ___( 1 )
40% of a + 70% of b = 52% of 20 grams
⇒ 0.40a + 0.70b = 10.4 ___( 2 )
Substitute the value of 'a' in equation ( 2 ) from (1) we get,
0.40( 20 - b ) + 0.70b = 10.4
⇒8 - 0.40b + 0.70b = 10.4
⇒ 0.30b = 10.4 - 8
⇒ b = 2.4 / 0.30
⇒ b = 8
⇒ a = 12
Therefore, the solution used by Serena for 40% is 12 grams and 70% solution is 8 grams.
The above question is incomplete , the complete question is:
Serena is making an experiment. For that, she needs 20 grams of a 52% solution of salt. She has two large bottles of salt water: one with 40% and the other with 70% of salt in them. How much of each must she use to make the solution she needs?
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Which graph represents the inequality y is less than negative one-third times x plus 1? The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line. The graph shows a dashed line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line. The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading below the line. The graph shows a dashed line, which crosses the y-axis at 1 and the x-axis at 3, with shading below the line.
The graph represents the inequality, the graph shows a dashed line, which crosses the y-axis at 1 and the x-axis at 3, with shading below the line.
What is linear inequality?According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. Any of the symbols for inequality, including greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).
Given the phrase, y is less than negative one-third times x plus 1
negative one-third times x plus 1,
-1/3x + 1
y < -1/3x + 1
to plot the coordinates consider,
y = -1/3x + 1
when x = 0, y = 1
and when y = 0,
0 = -1/3x + 1
-1/3x = -1
x = 3
x 0 3
y 1 0
and the graph says y is less than negative one-third times x plus 1,
so the shaded portion will be below the line, and the graph is attached for the condition.
Hence option D is correct.
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a company manufacturers soda cans with a diameter of 52 millimeters. in a sample of 12 cans, the standard deviation was 2.3 millimeters. what would be the 96% confidence interval for these cans?
The 96 % confidence interval for the cans, given the diameter and standard deviation, is (50.45, 53.55).
How to find the confidence interval ?The 96% confidence interval for the mean diameter of soda cans manufactured by the company can be calculated using the following formula:
= Mean ± (critical value x standard deviation / square root of sample size)
The critical value for a 96 % confidence interval is 2. 33 so the lower bound of the interval is:
= 52 - ( 2.33 x 2. 3 / √12 )
= 50. 45
The upper bound of the interval is:
= 52 + ( 2.33 x 2. 3 / √12 )
= 53. 55
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If line r through (1, 1) and (5, 7) is parallel to line s through (4, -2) and (x, y), what are possible values for x and y?
If line r through (1, 1) and (5, 7) is parallel to line s through (4, -2) and (x, y),
all the possible values of x and y are those values that satisfy the equation 3x - 2y = 16.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
Given:
If line r through (1, 1) and (5, 7) is parallel to line s through (4, -2) and (x, y),
then their slopes are equal.
(7 -1)/(5 - 1) = (y + 2)/(x-4)
3/2 = (y + 2)/(x-4)
3x - 12 = 2y + 4
3x - 2y = 16.
Therefore, all the values that satisfy the equation 3x - 2y = 16.
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A new product price is increased from $5 to $6. What is the percent of change?
Answer:
Step 1: $5 to $6 is a $1 increase
Step 2: Divide by the old value: $1/$5 = 0.2
Step 3: Convert 0.2 to percentage: 0.2×100 = 20% rise.
Or you could do it this way:
Step 1: Divide new value by old value: $6/$5 = 1.2
Step 2: Convert to percentage: 1.2×100 = 120% (i.e. $6 is 120% of $5)
Step 3: Subtract 100%: 120% − 100% = 20%, and that means a 20% rise.
Answer:
20%
Step-by-step explanation:
$5 to $6 is a $1 increase
Divide by old value: $1/$5=.2=20%
To check: $5 times 1.2 (120%)=6
2nd Method:
Divide by new vlaue: $6/$5=1.2
1.2=120%
120%-100%=20%
the measures of the angles in a triangle are in a ratio of 2:2:4. find the exterior angle that is adjacent to the largest triangle.
The exterior angle adjacent to the largest interior angle in a triangle with a 2:2:4 angle ratio is 90 degrees.
The exterior angle adjacent to the largest interior angle in a triangle is equal to the sum of the other two interior angles.
Let's call the measures of the angles in the triangle x, x, and 2x. Then,
x + x + 2x = 180 degrees,
so 4x = 180 degrees, and
x = 45 degrees.
The largest interior angle is 2x, or 90 degrees. The exterior angle that is adjacent to this angle is equal to 180 degrees minus the interior angle, which is 180 - 90 = 90 degrees.
So the exterior angle adjacent to the largest interior angle in a triangle with a 2:2:4 angle ratio is 90 degrees.
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please help ! i’m so confused
Answer:
7
Step-by-step explanation:
3^2 = 9
18-9=9
63÷ 9=7
Answer:
7
Step-by-step explanatio
63 ÷ (18-9)
63÷9= 7
You are applying for jobs at two companies. Company A offers starting salaries with $$ \mu = $31,000 $$ and $$ \sigma = $1000 $$ . Company B offers starting salaries with $$ \mu = $31,000 $$ and $$ \sigma = $5000 $$ . From which company are you more likely to get an offer of $33,000 or more? Explain your reasoning.
As a result, Company B is more likely to make you an offer of $33,000 or more than Company A.
What is standard deviation?The standard deviation in statistics is a measure of the degree of variation or dispersion in a set of values. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
Here,
To determine which company you are more likely to receive an offer of $33,000 or more, we need to look at the standard deviations of each company's starting salary. Company B has a standard deviation of $5000, which is 5 times greater than Company A's standard deviation of $1000. This means that the salaries offered by Company B are spread out over a larger range, with a higher chance of extreme values.
We can calculate the z-score for an offer of $33,000 from each company using the formula:
z = (x - μ) / σ
For Company A:
z = ($33,000 - $31,000) / $1000 = 2
For Company B:
z = ($33,000 - $31,000) / $5000 = 0.4
A z-score of 2 for Company A indicates that an offer of $33,000 is 2 standard deviations above the mean, which is relatively rare. On the other hand, a z-score of 0.4 for Company B indicates that an offer of $33,000 is only 0.4 standard deviations above the mean, which is much more likely.
Therefore, you are more likely to receive an offer of $33,000 or more from Company B than Company A.
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slope of the line that contains the following points: (17, -12) and (12, 8)
si por qué si y si por qué obvio si
Trapezoid WHNT id shown where R is the midpoint of HN, Y is the midpoint of WT.
WH = 10x +2.6,
NH = 11x- 7.4,
TN 23x -3.9,
RY = 18x- 4.1, and
WT = 8x + 5.2.
Answer:
It looks like you're trying to solve a problem involving geometry and algebra. To solve this problem, you need to use the information given in the statements to find the value of x and then use that value to find the lengths of the sides of the trapezoid.
Starting with the first statement, we have:
WH = 10x + 2.6
NH = 11x - 7.4
Next, we can use the information about Y being the midpoint of WT to find the value of WT:
WT = 2 * RY = 2 * (18x - 4.1) = 36x - 8.2
Using the information about R being the midpoint of HN, we can find the value of HN:
HN = 2 * RY = 2 * (18x - 4.1) = 36x - 8.2
Finally, using the information about TN, we can find the value of TN:
TN = 23x - 3.9
With these values, we can now find the lengths of the sides of the trapezoid. The length of the top side (WH) is 10x + 2.6, the length of the bottom side (TN) is 23x - 3.9, the length of the left side (NH) is 11x - 7.4, and the length of the right side (WT) is 36x - 8.2.
Note: To fully solve the problem, you will need to use the given equations to find the value of x.
To find the value of x, we need to equate the midpoint formula with the given expressions.
The midpoint formula is (x1 + x2)/2 = x and (y1 + y2)/2 = y.
We can use this formula to find the value of x.
For example, for the midpoint R:
x = (WT + NH)/2
x = (8x + 5.2 + 11x - 7.4)/2
x = (19x - 2.2)/2
x = 9.5x - 1.1
And for the midpoint Y:
y = (WH + TN)/2
y = (10x + 2.6 + 23x - 3.9)/2
y = (33x - 1.65)/2
y = 16.5x - 0.825
Now we have two equations:
9.5x - 1.1 = 16.5x - 0.825
7x = 0.725
x = 0.725/7
x = 0.104285714
So the value of x is approximately 0.104285714.
Answer:
Step-by-step explanation:0.1
What is halfway between 0.2 and 0.3
Help plsss
Answer:
0.25
Step-by-step explanation:
You are finding the average of the two numbers by finding the halfway point. So you do 0.2+0.3 = 0.5 and then you divide by 2. 0.5/2 = 0.25
Hope this helped :)
hat is the ratio of the area of a regular hexagon to the area of the hexagon which uses the midpoints of the first hexagon's sides as its vertices? express your answer as a common fraction.
The ratio of the area of a regular hexagon to the area of the smaller hexagon that uses its midpoints as vertices is 4:1. The common factor in this expression is 4
The closed polygonal shape of a regular hexagon has six equal sides and six equal angles. Any regular polygon has equal sides and angles on all sides. Regular pentagons, for instance, have 5 equal sides, and regular octagons have 8 equal sides. When these requirements are not met, polygons might resemble many other asymmetrical shapes. A regular hexagon is formed when six equilateral triangles are placed side by side. The regular hexagon's area then increases to six times that of the same triangle. In this post, let's learn about its features, the formula for area, and the perimeter.
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The pharmacist has a 2.8 L bottle of cough syrup. If she fills a bottle that is 1,200 ml, how many ml of cough syrup does the pharmacist have left? (1 L = 1,000 ml) 160 ml
Answer:
1600 mL
Step-by-step explanation:
if 1L = 1000mL then:
2.8L is equal to 2800mL
2800 - 1200 = 1600
show me how to solve this -4x less than 12
Answer:
Factor 4 out of 12+4x 4(3+x)
Step-by-step explanation:
Given the km represents an angle bias for, find the value of x and KL
Answer:
Answer is in attached photo.
Step-by-step explanation:
SolutionThe solution is in the attached photo, do note that to solve this question, there are multiple ways (using Pythagoras' Theorem), this is only one of the ways.
For each pair of equations, determine whether the second equation is the result of a valid operation on the first. If what is the operation.
1. 7 + 5x= 3 - 2x and 7 + 7x = 3
2. 3(x - 4) = 15 and x - 4 = 15
3. x^2 = 6x and x = 6
4. 1/(x - 5) = 10 and 1 = 10(x - 5)
^ this one is a fraction 1 over (x - 5)
The following pairs of equations have its second equation valid
7 + 5x= 3 - 2x and 7 + 7x = 3
1/(x - 5) = 10 and 1 = 10(x - 5)
The invalid equations are;
3(x - 4) = 15 and x - 4 = 15
x^2 = 6x and x = 6
How to calculate using mathematical operation?1. 7 + 5x= 3 - 2x and 7 + 7x = 3
Add 2x to both sides
7 + 5x + 2x = 3
7 + 7x = 3
Valid
2. 3(x - 4) = 15 and x - 4 = 15
3x - 12 = 15
Invalid
3. x^2 = 6x and x = 6
find the square root of both sides
√x² = √6x
x = √6x
Invalid
4. 1/(x - 5) = 10 and 1 = 10(x - 5)
cross product
1 × 1 = 10(x - 5)
1 = 10(x - 5)
Valid
Therefore, 7 + 5x= 3 - 2x and 7 + 7x = 3;
1/(x - 5) = 10 and 1 = 10(x - 5) are the valid equations.
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a football field is supposed to be exactly 120yd long, including the end zones. how many inches is this? (1yd
The length of a football field, including the end zones, is 120 yards, which is equal to 4320 inches.
To calculate this, we can use the conversion rate of 1 yard equal to 3 feet and 1 foot equal to 12 inches. This means that 1 yard is equal to 36 inches. To convert 120 yards to inches, we can multiply 120 by 36, resulting in 4320 inches.
To explain this mathematically, we can use the formula:
Inches = Yards x (Feet/Yard) x (Inches/Foot)where Inches/Foot = 12 and Feet/Yard = 3.
Plugging in the appropriate variables, we can calculate the number of inches in a football field as:
Inches = 120 x 3 x 12 = 4320 inches.
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A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 81 long and 55 wide. What is the length of a training track running around the field?
The length of a training track running around the field is 334.7m.
What is Rectangle?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
What is semicircle?A semicircle is created when a circle is divided in half along its diameter. There is an equal distribution of each half. A semicircle is a circle that has been folded in half; it is sometimes referred to as a half-disk.
here, we have,
GIven that;
length of rectangle = 81m
width of rectangle = 55m
Length of track running around the field = 2 x length of field + circumference of two semicircles
= 2 x 81 +pi x 55
= 162 + 3.14 x 55
= 334.7m
∴ the length of a training track field is 334.7m
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Triangle bac was dilated from triangle bde at a scale factor of 2. what proportion proves that cos∠d = cos∠a? triangles bde and bac, in which angle b is a right angle, point d is between points b and a, and point e is between points b and c; bd measures 2 units, be measures 3 units, and de measures 3 and 61 hundredths units. 2 over 3 and 61 hundredths = 4 over 7 and 22 hundredths three halves = six fourths 3 over 3 and 61 hundredths = 6 over 7 and 22 hundredths two thirds = four sixths
According to the solving triangle proportion proves that cos ∠d = cos ∠a is
3/3.61 = 6/7.22
What is triangles?A triangle seems to be a three-sided polygon with three vertices. The angles of both the triangle are formed by the connection of the three sides end to end at a single point. The triangle's three angles add up to 180 degrees.
According to the given information:
Right angled triangles BAC and BDE are comparable to one another.
This is due to the fact that when a shape is dilated, then new shape would resemble the previous shape but be smaller. Both shapes' angles are the same if they both stay the same.
Scale factor = 2
BE = 3, BD = 2, DE = 3.61
Each of the corresponding sides of ∆BDE will be multiplied to get each of the corresponding sides of ∆ABC.
BC = 2×BE = 2×3 = 6
AB = 2×DE = 2×3.61 = 7.22
See second diagram
sin ∠D = opposite/hypotenuse = BE/DE
BE/DE = 3/3.61
sin ∠A = BC/AC
BC/AC = 6/7.22
Therefore sin ∠D = sin ∠A
3/3.61 = 6/7.22 (C)
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Answer:3/3.61 = 6/7.22
Step-by-step explanation:
got it right on the test
Stacey is designing a custom rug for a client. the current design is a rectangle with a width of 8 feet and a length of 5 feet. the client wants the rug to be larger but doesn't want the width to exceed 12 feet. select any of the scale factors that stacey could use to dilate the current dimensions and meet the customer's requests.
Answer:87
Step-by-step explanation:
A builder is using the drawing below to build a house. If the owner decides to increase the living room dimensions by 20%, what is the new length and width of the living room floor?a. 14.4 feet x 9.6 feetb. 144 feet x 96 feetc. 13.2 feet x 8.2 feetd. 10 feet x 8 feet
Percentage increment means the part of original value is added to the value. The new length of the living room is 14.4 feet long and new width of the living room is 1.6 feet long. The option A is the correct option.
The length of the living room is 12 feet.
The width of the living room is 8 feet.
The owner increases the 20 percent of length and 20% width.
Suppose new length is feet long. As the owner increases the 20 percent of length. Thus the new length will be sum of original length and the 20 percent of it. Hence,
l=12+12/100*12
l=14.4
Thus the new length of the living room is 14.4 feet long.
Suppose new width is feet long. As the owner increases the 20 percent of width. Thus the new width will be sum of original width and the 20 percent of it. Hence,
w=8+20/100*8
w=9.6
the new width of the living room is 1.6 feet long.
Hence the new length of the living room is 14.4 feet long and new width of the living room is 1.6 feet long.
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uppose a person sitting in the front, middle portion of the class is randomly selected to answer a question. find the probability that the person selected is female.
There is a 50% chance that the person selected is female.
Let's assume that there are 50 students in the class and of them, 25 are female and 25 are male.
The probability that the person selected is female will be calculated by the formula P(Female) = 25/50 = 0.5
Therefore, the probability that the person selected is female is 0.5 or 50%. This means that if a person is randomly selected from the front, middle portion of the class, there is a 50% chance that the person selected is female.
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Complete question:
What is the gender ratio of the people in the class?