The average number of viewers over the two weeks will be 3.85 × 10⁴.
How to calculate the value?It should be noted that based on the information, the TV show had 3.6 x 10⁴ viewers in the first week and 4.1 x 10⁴ viewers in the second week.
Therefore, the average number of viewers over the two weeks will be:
= [(3.6 × 10⁴) + (4.1 × 10⁴)] / 2
= 3.85 × 10⁴
Therefore, the average number of viewers over the two weeks will be 3.85 × 10⁴.
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shonda went for a drive in her new car. She drove for 147.5 miles at a speed of 59 miles per hour. For how many hours did she drive?
Answer:
2.5
Step-by-step explanation:
By Using s = d/ t
So t = d / s
t = 147.5 / 59= 2.5This is a conversion graph between litres and gallons. Use the graph to convert 60 gallons to litres
Disclaimer: The conversion graph is missing in the question.
60 gallons is equal to 227.125 litres.
Refer to the attached image for the conversion of litres to gallons.
And gallons to litres.
In this image, a vertical line is drawn from the given value of gallon until it meets the cross line. And then a horizontal line is drawn, which touches the litres line.
At the point at which this horizontal line touches the litres line, that value is considered as the corresponding litres for the given gallons.
Similarly, a vertical line is drawn from the litres line until it meets the cross line. And then a vertical line is drawn, which touches the gallons line.
At the point at which this vertical line touches the gallons line, that value is considered as the corresponding gallons for the given litres.
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.Solve 2x−1<4 or −5x−3>−3 and write the solution in interval notation.
The interval notation is { 5/ 2 < x > 0 }
How to determine the valueGiven the inequalities;
2x−1<4−5x−3>−3To determine the value of x, we have;
2x - 1 < 4
collect like terms
2x < 4 + 1
2x < 5
Make 'x' the subject
x < 5/ 2
−5x −3 > −3
collect like terms
-5x > -3 + 3
-5x > 0
x > 0
Thus, the interval notation is { 5/ 2 < x > 0 }
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fx(7)(87x+7y)(5)⁴is equal to the root of?
The area of a certain desert (Desert 1) is eight times the area of another desert (Desert 2). If the sum of their areas is
27,000,000 square miles, find the area of each desert.
What is the area of Desert 1?
Answer:
1687500
Step-by-step explanation:
If their sum is 27,000,000 then their are millions of ways to find this answer. like one can be 13500000. But that answer is obviously incorrect. If you divide that by 8, your answer will be 1687500.
A baby American bison weighs 20kg. A baby blue whale weighs 100 times as great as a baby American bison. how much does a baby blue whale weigh
a baby blue whale weigh= 2000 kg
Simple equation :
A linear equation that involves only one variable is known as a simple equation or a linear equation in one variable. For example, \(3x + 2 = 23,x = 7,2x + 6 = 3x – 4,\)etc., are simple equations.Let us assume a situation, in which you go to the market to buy mangoes in a supermarket. Your mother gave you Rs.100 and said that you can keep Rs.40 for buying chocolates and for the remaining amount, you need to buy mangoes. When you went to the market, you found out that the price of one kg of mangoes was Rs.12. So, the final question is how many mangoes you should buy, so that everyone is satisfied. Recall the concept of simple equations from previous classes and proceed. Let us assume that you have to purchase kg of mangoes, so the total amount of money that you will be spent on buying mangoes will be Rs.12x. Now, you have Rs.40 for yourself, so you have an equation:
12 x + 40 = 100
12x = 100 – 40
12x = 60
x = 60/12 = 5, This is the same equation as above. Now when you will solve this, you will get to know the value of 5kg of mangoes. It means that you can buy 5 kg mangoes and spend Rs.40 on buying chocolates
weigh: to measure how heavy something is, especially by using a machine (scales)
given :
A baby American bison weighs=20kg
The solution according to Question =
Let the weight of baby blue whale = b
the baby blue whale weighs =100(a baby American bison)
b=100(20)
b=2000 weigh
a baby blue whale weigh= 2000 kg
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X^2+7x=8 find the solutions
The value of x is 1 and -8.
To solve this problem we need to understand the concept of quadratic equation.
To solve Quadratic equation we need to understand the concept of equation which says the factor of the product of coefficient of [tex]x^{2}[/tex] and constant must on adding or substracting give the coefficient of x.
Here the equation is [tex]x^{2} +7x-8=0[/tex]
The product of coefficient is 8. The factors of 8 is 8 and 1 which gives 7 on substracting.
Now,
[tex]x^{2} +8x-x-8=0[/tex]
⇒[tex]x(x+8)-1(x+8)=0\\[/tex]
⇒[tex](x-1)(x+8)=0[/tex]
∴ x=1,-8.
So, the required values of x is 1 and -8.
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The length of a rectangle is 3m less than double the witch, and the area of the rectangle is 27m^2. Find the dimensions of the rectangle.
Answer:
the area of the rectangle is A=L•W
The length is 3m less than twice its width W: L+ 3m=2W...->, L=2W-3m
A=L-W
27m²=(2W-3m)-W
27m2=2w2-3m-W
2w2-3wm-27m2=0
....use quadratic formula -(-3m)+ (-3m)²-4-2-(-27m²)
W=
2-2
w=(3m± √9m²+216m²)
w=(3m+ √225m²)
W=(3m± 15m...you need only positive root because width cannot be negative
W= 3m+15m
4
W=. 4
18m
W=4.5m ......now find the L
L=2.4.5m-3m
L=9m-3m
L=6m
Answer:
W = 4.5cm
L = 6cm
Step-by-step explanation:
Ride tickets at the fair can be bought in
packs of 5 tickets for $8.75 or 3 tickets for
$6.25. Simone wants to buy 15 tickets. At
these rates, how much more will she spend
if she only buys packs of 3 tickets?
She will spend 5 dollars extra if she only buys packs of 3 tickets.
What is a numerical expression?A numerical expression is written in form of numbers and their operations.
According to the given question we can buy 15 tickets in two ways either buying 5 packs which contain 3 tickets and cost 6.25 dollars each pack or we can buy 3 packs which contain 5 tickets which costs 8.75 dollars.
For the first case if we buy 5 packs of tickets that contain 3 tickets it will cost (5×6.25) dollars = 31.25 dollars.
In the second case buying 3 packs of tickets that contain 5 tickets that will cost us (3×8.75) = 26.25 dollars.
∴ She will spend (31.25 - 26.25) = 5 dollars she will spend extra if she only buys packs of 3 tickets.
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Part 2 of 2
You invested $15,000 in two accounts paying 4% and 7% annual interest, respectively. If the total interest earned for
the year was $960, how much was invested at each rate?
$3000 and $12000
If you know the principal amount, the rate of interest, and the time periods, you can use the simple interest formula to calculate the interest.
The following is a simple interest formula:
SI = P *R * T /100
Where SI = simple interest
Principal (P)
interest rate, or R (in percentage)
T is the time period (in years)
The following formula is used to determine the overall sum:
Sum (A) = Principal (P) + Interest (I)
Where,
The entire amount repaid at the conclusion of the borrowing period is indicated by the letter (A).
You can also write the total amount formula for simple interest as follows:
A = P(1 + RT)
X+Y = $15000
0.04x + 0.07y = 960
0.04x + 0.07 ( 15000 - x) = 960
0.04x + 1050 - 0.07x = 960
0.03x = 90
x = $3000
y= $12000
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5. A population with mean = 37 and standard deviation = 6 is standardized so that the new mean is 50 and the new standard deviation is 10. A scale of 40 on the first scale is equivalent to what score on the new standardized scale?
Using z-scores, it is found that a scale of 40 on the first scale is equivalent to a score of 55 in the new standardized scale.
What are z-scores?The z-score of a measure X of a distribution with mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is above(in case the score is positive) or below(in case the score is negative) the mean. Looking at the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.For the first scale, the parameters are given as follows:
[tex]X = 40, \mu = 37, \sigma = 6[/tex]
Hence the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (40 - 37)/6
Z = 0.5.
For the second scale, we want to find X when Z = 0.5, considering the following mean and standard deviation:
[tex]\mu = 50, \sigma = 10[/tex]
Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
0.5 = (X - 50)/10
X - 50 = 5
X = 55.
A scale of 40 on the first scale is equivalent to a score of 55 in the new standardized scale.
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Two planes, which are 2940 miles apart, fly toward each other. Their speeds differ by 35mph. If they pass each other in 4 hours, what is the speed of each?
Answer:
385 mph350 mphStep-by-step explanation:
You want the individual speeds of airplanes that close the 2940 mile distance between them in 4 hours, and have a speed difference of 35 mph.
SetupThe closing speed is found using the relation ...
speed = distance/time
It is ...
(2940 mi)/(4 h) = 735 mi/h
If x represents the speed of the slower plane, then (x+35) is the speed of the faster one. The sum of their speeds is the closing speed:
x +(x +35) = 735
SolutionSimplifying, we have ...
2x +35 = 735
2x = 700 . . . . . . subtract 35
x = 350 . . . . . . . divide by 2
x+35 = 385 . . . . speed of the faster plane
The speeds of the planes are 350 mph and 385 mph.
a 3 gallon bottle of bleach costs 15.84. what is the price per cup?
Answer: $0.33 per cup
Step-by-step explanation:
15.84/3 to find the price per 1 gallon.
15.84/3 = 5.28 per gallon
There are 16 cups in a gallon, so divide the price of a single gallon by 16.
5.28/16 = price per cup
5.28/16 = .33
The price for each cup of bleach is $0.33.
I need help with math ngl
Answer:
Oldest to newest:
10^-35, 10 ^-10, 0
Step-by-step explanation:
Scientific notation
To figure out the power of 10 think "how many places do I move the decimal point?"
When the number is 10 or greater the decimal point moves to the left, and the power of 10 is positive.
When the number is smaller than 1 the decimal point moves to the right, so the power of 10 is negative.
You invested $27,000 in two accounts paying 4% and 7% annual interest, respectively. If the total interest earned for the year was $1440 how much was invested at each rate?
a = amount invested at 4%.
b = amount invested at 7%.
we know that whatever "a" and "b" may be, they total 27000, so we can say that a + b = 27000, likewise we can say that b = 27000 - a.
how much will it be for 4% of "a"? well, that's just (4/100) * a, or 0.04a.
how much will it be for 7% of "b"? well, that's just (7/100) * a, or 0.07b.
we also know that the earned interest by those two interest amounts is 1440, so
[tex]\begin{cases} a + b = 27000\\ b = 27000 - a \end{cases}\hspace{5em}0.04a~~ + ~~0.07b~~ = ~~1440 \\\\\\ \stackrel{\textit{substituting "b"}}{0.04a~~ + ~~0.07(27000-a)~~ = ~~1440}\implies 0.04a+1890-0.07a=1440 \\\\\\ 1890-0.03a=1440\implies -0.03a=-450\implies a=\cfrac{-450}{-0.03} \\\\\\ 15000=\textit{\LARGE a}\hspace{15em}\stackrel{27000~~ - ~~15000}{\textit{\LARGE b}=12000}[/tex]
Sandra bought 4 bars of chocolate and a packet of nuts for $11.50. If a bar of chocolate costs $0.50 less than a packet of nuts, find the cost of a packet of nuts
Answer:
A packet of nuts costs $2.70
Step-by-step explanation:
Let C represent the cost of a bar of chocolate and P represent the cost of a packet of nuts
4 bars of chocolate will cost $4C
1 packet of nuts costs $P
Total price Sandra paid is $11.50
This can be represented using
4C + P = 11.50 (1)
A bar of chocolate costs $0.50 less than a packet of nuts. So
P - C =0.50
-C + P = 0.50 (2)
Multiply eq (2) by 4 to get
-4C + 4P = 4 x 0.50
-4C + 4P = 2 (3)
Add equations (1) and (3) to eliminate the 4C term
4C + P - 4C + 4P = 11.50 + 2
P+4P = 13.50
5P = 13.50
Dividing by 5 on both sides
5P/5 = 13.50/5
P = 2.70
So a packet of nuts costs $2.70 (Answer)
To verify this is correct,
Use equation (2) to get
-C + P = 0.50
-C + 2.70 = 0.50
Add C to both sides
-C + 2.70 + C = 0.50 + C
2.70 = 0.50 + C
Subtract 0.50 from both sides
2.70-0.50 = 0.50 + C - 0.50
2.20 = C which is C= 2.20
Plug this value into equation (1)
4(2.20) + 2.70 = 8.80 + 2.70 = 11.50
So verified that answers are correct
Let S be the universal set, where:
S = {1, 2, 3, ..., 18, 19, 20}
Let sets A and B be subsets of S, where:
Set A = {7, 9, 12, 13, 14}
Set B =
{1, 4, 5, 7, 16, 18, 19}
Set C= {4, 6, 8, 9, 11, 13, 15, 16, 17, 19}
LIST the elements in the set (AUBUC)
(AUBUC) = {
-Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE
LIST the elements in the set (An BnC)
(An BnC) = {
}
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE
You may want to draw a Venn Diagram to help answer this question.
The elements of (A∪B∪C) = {1, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19}
The elements of (A∩B∩C) = DNE
SetsFrom the question, we are to list the elements of the given sets
From the given information,
Set A = {7, 9, 12, 13, 14}
Set B = {1, 4, 5, 7, 16, 18, 19}
Set C = {4, 6, 8, 9, 11, 13, 15, 16, 17, 19}
We are to list the elements of (A∪B∪C)
(A∪B∪C) = {1, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19}
Also, we are to list the elements of (A∩B∩C)
(A∩B∩C) = { } OR ∅
Since this is an empty set
(A∩B∩C) = DNE
Hence,
The elements of (A∪B∪C) = {1, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19}
The elements of (A∩B∩C) = DNE
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Find the slope of (8,9) and (23,9)
Step-by-step explanation:
you mean the slope of the line between (8, 9) and (23, 9).
we can see that right away, as the y value does not change. it means it is a flat line, and that means the slope is 0.
now, formally :
the slope of a line is (y coordinate change / x coordinate change) when going from one point on the line to another.
the direction does not matter, but once we pick one for the comparison of one coordinate, we have to use the same direction also for the other.
I prefer to go from left to right.
so, from (8, 9) to (23, 9).
x changes by +15 (from 8 to 23).
y changes by 0 (from 9 to 9).
the slope is therefore 0/+15 = 0.
R,S,Q and P are midpoints of OC, Cb, BA and OA OR=a CS=b and OP=c show that RS is parallel to PQ PLS HELP
1 fluid oz = ______
please answer asap
Find the mystery number. It is a common multiple of 2,5 and 7. It has 3 digits. The sum of the digits is 10. The number is less than 500
The number is 280
In mathematics, Least Common Multiple is referred to by its entire name, whereas Highest Common Factor is its complete name. The L.C.M. defines the least number that is exactly divisible by two or more numbers, whereas the H.C.F. describes the biggest factor existing between any given pair of two or more numbers. LCM is also known as the Least Common Multiple (LCM), and HCF is also known as the Greatest Common Factor (GCF).
Two key techniques—the division method and the prime factorization approach—can be used to determine H.C.F. and L.C.M.
So we need to find the LCM of 2,5 and 7. Furthermore, we need to find multiply the LCM with a number which can make its sum of digits equal to 10.
LCM of 2,5 and 7 is 70
70 x 4 = 280
Sum of digits of 280 is 10, which is also less than 500
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Graph the image of △RST after a reflection over the line y=x.
Answer:
Put S=(1,-10) R(-10,-8) T(-8,-9) Make sure to put a ´ after these letters when you put them down
Step-by-step explanation:
How much will each person get if 5 people share 1/3 a pond of candy
[tex]\stackrel{\textit{lbs of candy}}{\cfrac{1}{3}}\div \stackrel{people}{5}\implies \cfrac{1}{3}\div\cfrac{5}{1}\implies \cfrac{1}{3}\cdot \cfrac{1}{5}\implies \stackrel{\textit{lbs of candy}}{\cfrac{1}{15}}[/tex]
A rectangle has a perimeter of 50 feet. The length is 5 feet more than the width. Find the width and length of the rectangle.
The width of the rectangle = 10 ft
The length of the rectangle = 15 ft.
What is the Perimeter of a Rectangle?The formula for the perimeter of a rectangle is given as:
Perimeter = 2(length + width).
Let x represent the width of the rectangle
Width of the rectangle = x
Length of the rectangle = x + 5
Perimeter of the rectangle = 50 ft
Thus, we would have the following equation:
2(x + 5 + x) = 50
2(2x + 5) = 50
4x + 10 = 50
4x = 50 - 10
4x = 40
4x/4 = 40/4
x = 10
Width of the rectangle = x = 10 ft
Length of the rectangle = x + 5 = 10 + 5 = 15 ft.
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What number multiplied by 7/9 as a product of one
The number multiplied by 7/9 to get a product of one will be 9/7.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
Suppose the number when multiplied by 7/9 as a product of one be x,
When the product of two numbers is 1, they are termed multiplicative inverses. To make the expressions simpler, use the multiplicative inverse. When we solve division problems, the multiplicative inverse is one application. When dividing two numbers, the dividend is multiplied by the reciprocal of the divisor.
x × 7/9 = 1
x=9/7
Thus, the number multiplied by 7/9 to get a product of one will be 9/7.
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Translate this phrase into an algebraic expression.
The sum of 17 and twice Matt's score
Use the variable m to represent Matt's score.
Answer:
17 + 2 x m
Step-by-step explanation:
sum is to add and twice is to multiply by 2
How many kg of peanuts must Heather
add to 4 kg of mixed nuts containing 60%
peanuts to make a mixture with 92%
peanuts?
37.375 kg of peanuts must be added to the 4 kg of mixed nuts to make a mixture containing 92 % of peanuts.
Total mixture of mixed nuts = 4 kg
60 % of them are peanuts.
So, we will calculate the percentage:
Let x be the amount of peanuts.
60 / 100 x = 4 kg
0.6 x = 4 kg
x = 4 kg / 0.6
x = 6.67 kg
Now let the peanuts added be y
So, 92 % of ( 4 kg + y ) should be peanuts.
So, we get the equation as:
0.92 ( 4 ) + 0.92 y = 6.67 + y
3.68 + 0.92 y = 6.67 + y
0.08 y = 2.99
y = 37.375 kg
Therefore, 37.375 kg of peanuts must be added to the 4 kg of mixed nuts to make a mixture containing 92 % of peanuts.
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Convert 50°F to degrees Celsius.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C=5/9(F-32)
F=9/5C+32
Answer:
10°C
Step-by-step explanation:
F = 50
C = 5/9 * (F - 32) = 5/9 * (50 - 32) = 5/9 * 18 = 5 * 2 = 10
Yard Professionals Inc. experienced the following events in Year 1, its first year of operation:
Performed services for $26,500 cash.
Purchased $7,200 of supplies on account.
A physical count on December 31, Year 1, found that there was $1,510 of supplies on hand.
Required
Based on this information alone:
Record the events under an accounting equation.
Prepare an income statement, balance sheet, and statement of cash flows for the Year 1 accounting period.
What is the balance in the Supplies account as of January 1, Year 2?
What is the balance in the Supplies Expense account as of January 1, Year 2?
1. Recording the events under an accounting equation is as follows:
Assets = Liabilities + Equity
Cash + Supplies Common Stock + Revenue - Expenses
1. $26,500 $26,500
2. $7,200 $7,200
3. (5,690) ($5,690)
Balance $26,500 $1,510 $7,200 $26,500 - $5,690
2. The preparation of the income statement, balance sheet, and statement of cash flows for the Year 1 accounting period is as follows:
Yard Professionals
Income StatementFor the Year 1 accounting period
Revenue $26,500
Supplies Expense (5,690)
Net income $20,810
Yard Professionals
Balance SheetYear 1 accounting period
Cash $26,500
Supplies $1,510
Total assets $28,010
Accounts Payable $7,200
Equity: Net income 20,810
Total liabilities + equity $28,010
Yard Professionals
Statement of Cash FlowsFor the Year 1 accounting period
Net income $20,810
Supplies (1,510)
Accounts Payable 7,200
Cash (Operations) $26,500
3. The balance in the Supplies account as of January 1, Year 2 is $1,510.
4. The balance in the Supplies Expenses account as of January 1, Year 2 is $5,690.
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To two decimal places,
√70
must lie between ____
and _____.
To two decimal places ✓70 just be between 8.36 and 8.37.
How to illustrate the information?It should be noted that we simply have to calculate the information is to find the square root of 70.
Therefore, this is approximately 8.366
Therefore, to two decimal places ✓70 just be between 8.36 and 8.37.
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