Answers
Answer:
let the children be x
let the dog be y
for the heads
x+y = 14 --- eqn 1
for the legs
2x + 4y = 40 ----- eqn2
since the children have 2 legs each and the dogs have 4 legs each
x + y = 14
2x+4y=40
through elimination method
multiply eqn1 by 2 and multiply eqn2 by 1
2x + 2y = 28
2x + 4y = 40 , then subtract
-2y = -12
to get y divide both sides by -2
y = 6
since in eqn 1
x+y=14
x = 14-y = 14-6 = 8
x = 8, y = 6
the children are 8 while the dogs are 6
Related Questions
esson Quiz
The ages, in years, of 6 volunteers at the local food pantry are listed below. If a 7th volunteer joins them, what would their age be so that the range of their ages will be 557
(56, 81, 54, 47, 45, 94)
O
S
8
18
10
Answers
The age of the 7th volunteer has to be 602 years so that the range of the all volunteer ages will be 557.
Given ages of 6 volunteers = (56, 81, 54, 47, 45, 94)
The range = maximum value - minimum value.
So, range of the given list = 94 - 45 = 49.
To increase, the range to 557, we have to add an age that is greater than 94, To obtain that age we have to solve 557 - 45 = 508. [here 557 is the maximum value]
Now, by adding the obtained range to the 94 we can get the required age of 7th volunteer. So 508 + 94 = 602.
From the above explanation, we can conclude that the age of the 7th volunteer has to be 602 years which is unrealistic so that the range becomes 557.
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find two numbers who’s product is -9 and who’s sum is -8
Answers
Answer:
1, -9
Step-by-step explanation:
xy = -9
x + y = -8 solve this for x and substitute into the 1st equation
x = -8 - y
(-8 - y)y = -9
-y² - 8y + 9 = 0
y² + 8y -9 = 0
Solve for y by factoring:
(y - 1)(y + 9) = 0
y = 1, -9
x(1) = -9
x = -9
x(-9) = -9
x = -9/-9 = 1
Find m so that x + 5 is a factor of - 3x^4 - 10x^3 + 20x^2 - 22x + m.
Answers
If x + 5 is a factor of the given polynomial, then (x + 5) must divide the polynomial evenly, meaning that the remainder is 0 when the polynomial is divided by x + 5.
We can use polynomial long division or synthetic division to find the quotient and remainder, but it's easier to use the fact that if x + 5 is a factor, then (-5) must be a root of the polynomial.
So, we can substitute x = -5 into the polynomial and set it equal to 0 to find m:
-3(-5)^4 - 10(-5)^3 + 20(-5)^2 - 22(-5) + m = 0
Simplifying and solving for m:
-3(625) + 10(125) + 20(25) + 110 + m = 0
-1875 + 1250 + 500 + 110 + m = 0
m = 1015
Therefore, m = 1015 so that x + 5 is a factor of - 3x^4 - 10x^3 + 20x^2 - 22x + m.
what is the mode of 14, 17, 21, 28, 40
Answers
Answer:
24
Step-by-step explanation:
14 + 17 + 21 + 28 +40 / 5
120 / 5
24
A researcher claims that the proportion of smokers in a certain city is less than 20%. To test this claim, a random sample of 700 people is taken in the city and 150 people indicate they are smokers.
The following is the setup for this hypothesis test:
H0:p=0.20
Ha:p<0.20
In this example, the p-value was determined to be 0.828.
Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%)
Answers
Answer:
Based on the hypothesis test conducted with a significance level of 5%, we fail to reject the null hypothesis that the proportion of smokers in the city is 20%. This means that we do not have sufficient evidence to conclude that the proportion of smokers is less than 20%. The p-value of 0.828 suggests that there is a high probability that the observed proportion of smokers in the sample is due to chance and not a true difference in the proportion of smokers in the population. Therefore, we cannot conclude that the city has a lower proportion of smokers than 20%.
In this hypothesis test set up by the researcher, the p-value is 0.828, which is greater than the significance level (0.05). Therefore, we do not reject the null hypothesis, meaning there is not enough statistical evidence to validate the researcher's claim that the proportion of smokers is less than 20%
Explanation:A hypothesis test in statistics uses test statistics based on sample data to accept or reject a null hypothesis. In this scenario, the null hypothesis (H0) states that the proportion of smokers (p) is 20%. The alternative hypothesis (Ha) claims that the proportion of smokers is less than 20%. The p-value is a measure of the probability that the observed data could occur under the null hypothesis. In our case, a p-value of 0.828 means that there is an 82.8% chance of observing the data if the true proportion of smokers is 20%, or higher.
Usually a threshold known as the significance level (in this case 5% or 0.05) is used to determine whether the null hypothesis should be rejected or not. If the p-value is less than or equal to the significance level, it suggests that the observed data is inconsistent with the null hypothesis, and the null is usually rejected. However, since our p-value is greater (0.828 > 0.05), we would not reject the null hypothesis, suggesting that there is not enough evidence to support the researcher's claim that the proportion of smokers is less than 20%.
Therefore, the conclusion is that the researcher's claim cannot be validated using the provided data.
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PLEASE HELP ME WITH THE WHOLE PROBLEM PLEASEEEE
Answers
The probability of getting blue or green is 1/3, the probability of getting blue is 3/4 and there are 8 blue marbles.
What is the probability in each case?a) If the probability of getting a yellow marble is 2/3, then the probability of getting a blue or green marble is:
P(blue or green) = 1 - P(yellow) = 1 - 2/3 = 1/3
b) If the probability of getting a green marble is 1/4, then the probability of getting a blue marble is:
P(blue) = 1 - P(green) = 1 - 1/4 = 3/4
c) The total number of marbles in the bag is 24. Let x be the number of blue marbles. Then the number of yellow marbles is 2x, and the number of green marbles is 24 - x - 2x = 24 - 3x. We know that:
2x/24 = 2/3 (probability of getting a yellow marble is 2/3)
=> x = 8
Therefore, there are 8 blue marbles in the bag.
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Yogi is installing carpet in the hotel lobby. He Charges 4.30$ per square foot for the carpet plus $75 installation fee what is the total cost
Answers
If Yogi Charges 4.30$ per square foot for the carpet plus $75 installation fee, the total cost of installing carpet in the hotel lobby with Yogi is $2,225.
To determine the total cost of installing carpet in the hotel lobby with Yogi, we need to know the area of the lobby in square feet. Once we have the area, we can use Yogi's pricing scheme to calculate the total cost.
Assuming that we have measured the area of the lobby to be 500 square feet, we can calculate the total cost as follows:
Cost of carpet = area × price per square foot
= 500 × $4.30
= $2,150
Cost of installation = $75
Total cost = cost of carpet + cost of installation
= $2,150 + $75
= $2,225
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2. How does making tables help you
identify relationships between terms in
patterns?
Answers
Answer:
Step-by-step explanation:
well if you know the term than you know the pattern
Use the even and odd properties of the following functions to answer the questions:
a) If secθ=-3.1,then sec(-θ)=?
b)If sinθ=0.62,then sin(-θ)=?
Answers
Answer:
[tex]sec(-\theta)=-3.1[/tex]
[tex]sin(-\theta)=-0.62[/tex]
Step-by-step explanation:
Part a.
[tex]sec(\theta)[/tex] is related to [tex]cos(\theta)[/tex] through a reciprocal relationship [tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex].
Since [tex]cos(\theta)[/tex] is an even function (reflecting left-right across the y-axis doesn't change the graph), then [tex]sec(\theta)[/tex] is also an even function.
For any input in the domain, even functions produce the same output if the opposite of the input is used. In other words, if "f" is an even function, for all x in the domain of f, [tex]f(x)=f(-x)[/tex].
Thus, for the secant function, if a mystery value "x" is used as an input, and -3.1 is obtained as an output, then if the opposite of x, or -x, is input into the secant function, the output will also be -3.1.
[tex]sec(-\theta)=-3.1[/tex]
Part b.
The [tex]sin(\theta)[/tex] function does not reflect left-right across the y-axis to produce the same graph, so the sine function is not even.
However, the sine function can be rotated 180 degree about the origin, sometimes thought of as reflecting through the origin, to produce the same graph. Visually, this is an "odd" function.
For any input in the domain, if the opposite of the input is used, odd functions produce the opposite of the original output. In other words, if "g" is an odd function, for all x in the domain of g, [tex]-g(x)=g(-x)[/tex].
Thus, for the sine function, if a mystery value "x" is used as an input, and 0.62 is obtained as an output, then if the opposite of x, or -x, is input into the sine function, the output will be the opposite of 0.62, meaning -0.62.
[tex]sin(-\theta)=-0.62[/tex]
Solve and check: 3/4h+11=20 helpp!
Answers
Answer: 12
Step-by-step explanation:
We have to find h so the first step is to subtract the 11 from the 20
3/4h=9
Then to move the 3/4 over to the other side, you must multiply it by it's reciprocal, 4/3.
h= 4/3 x 9
This equals 12.
Assume that women's heights are normally distributed with a mean given by μ = 63.6 in, and a standard deviation given by a = 2.5 in. Complete parts a and b.
a. If 1 woman is randomly selected, find the probability that her height is between 62.9 in and 63.9 in.
The probability is approximately
(Round to four decimal places as needed.)
Answers
The probability that the woman's height is between 62.9 in and 63.9 in is 0.1580
Calculating the probability of values from the the z-scoresFrom the question, we have the following parameters that can be used in our computation:
Mean = 63.6Standard deviation = 2.5Age = between 62.9 and 63.9So, the z-scores are
z = (62.9 - 63.6)/2.5 = -0.28
z = (63.9 - 63.6)/2.5 = 0.12
i.e. between a z-score of -0.28 and a z-score of 0.12
This is represented as
Probability = (-0.28 < z < 0.12)
Using a graphing calculator, we have
Probability = 0.1580
Hence, the probability is 0.1580
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In a survey, 54.5% of respondents have portable earbuds and 30% of the respondents who have portable earbuds also have a smart speaker. What is the probability that a respondent has both portable earbuds and a smart speaker? If necessary, round to the nearest hundredth of a percent.
Answers
The probability that a respondent has both portable earbuds and a smart speaker is 0.16
What is the probability that a respondent has both portable earbuds and a smart speaker?From the question, we have the following parameters that can be used in our computation:
54.5% of respondents have portable earbuds 30% of the respondents who have smart speaker.This means that
P(earbuds) = 54.5%
P(smart speaker) = 30%
Using the above as a guide, we have the following:
P = P(earbuds) * P(smart speaker)
Substitute the known values in the above equation, so, we have the following representation
P = 54.5% * 30%
Evaluate
P = 0.16
Hence, the probability is 0.16
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What’s x+2(7-x)=12 but like this ( , )
Answers
The solution to the equation x + 2(7 - x) = 12 is x = 2.
What is the solution to the given equation?Given the equation in the question:
x + 2(7 - x ) = 12
To solve the equation, you need to use algebraic techniques to isolate the variable x on one side of the equation.
x + 2(7 - x) = 12
Apply distributive property
x + 2×7 + 2×-x = 12
x + 14 - 2x = 12
Combine like terms by subtracting 14 from both sides:
x - 2x = 12 - 14
-x = -2
Solve for x by dividing both sides by -1:
-x/-1 = -2/-1
x = 2
Therefore, the value of x is 2.
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50 Points! Multiple choice algebra question. Which function represents exponential growth? Photo attached. Thank you!
Answers
The exponential growth model is represented by the function y = 10 · 3ˣ. (Correct choice: D)
What function is an exponential growth function?
In this problem we must determine what function does represent an exponential growth model. With this purpose, we must define and understand the following functions:
Exponential growth model
y = a · rˣ, for r > 1.
Exponential decay model
y = a · rˣ, for 0 < r < 1.
Polynomic model
y = ∑ cₙ · xⁿ
The function y = 10 · 3ˣ represents an exponential growth model.
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Assistance needed pls and thanks
Answers
By using the parallelogram method, the addition of the vectors [tex]\vec a + \vec b[/tex] is (3, 1).
How to add vectors by using the head to tail method or parallelogram method?In Mathematics, a vector typically comprises two (2) points. First, is the starting point which is commonly referred to as the "tail" and the second (ending) point that is commonly referred to the "head."
Furthermore, the head to tail method of adding two (2) vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).
By adding the given vectors algebraically, we have the following:
[tex]\vec a + \vec b[/tex] = (2, -3) + (1, 4)
[tex]\vec a + \vec b[/tex] = [(2 + 1), (-3 + 4)
[tex]\vec a + \vec b[/tex] = (3, 1).
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Question 10 of 10
A minor arc will have a measure that is
O A. less than 180°
B. equal to 180°
OC. more than 180°
Answers
Answer:
Less than 180
Step-by-step explanation:
Minor: Less than 180
Major: More than 180
Find the missing side lengths. Leave your answers as radicals in simplest form.
Answers
Answer:
In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg, and the length of the hypotenuse is twice the length of the shorter leg.
[tex]n = \frac{2}{ \sqrt{3} } = \frac{2 \sqrt{3} }{3} [/tex]
[tex]m = \frac{4 \sqrt{3} }{3} [/tex]
what is the area of a circle with the diameter of 22 in
Answers
Answer:380.1 square inches
Step-by-step explanation:Area of a circle in terms of diameter: Area = π· (d2) 2 = 3.14· (222) 2 = 3.14· (11) 2 = 380.1 square inches (*)
Which expression is equivalent to 5(6x + 3y)?
A 11x+3y
B 11x+8y
C 30x+3y
D 30x+15y
Answers
Answer:
The answer is **D. 30x+15y**.
```
5(6x + 3y) = 5*6x + 5*3y = 30x + 15y
```
Step-by-step explanation:
1. Distribute the 5:
```
5(6x + 3y) = (5 * 6x) + (5 * 3y)
```
2. Simplify:
```
5(6x + 3y) = 30x + 15y
```
Therefore, 5(6x + 3y) is equivalent to 30x + 15y.
College Level Trig Question Any help will do!!
Answers
The value of x in the equation y = 9 sec(2x) at [0, π/4) ∪ (π/4, π/2] is x = 1/2[sec₋¹(y/9)]
Calculating the values of xFrom the question, we have the following parameters that can be used in our computation:
y = 9 sec(2x)
The interval of x is also given as
[0, π/4) ∪ (π/4, π/2]
This means that the values of x is from 0 to π/2, however, the function is undefined at x = π/4 i.e. there is a hole at x = π/4
Next, we set the equation to y
So, we have
9 sec(2x) = y
Divide both sides by 9
sec(2x) = y/9
Take the arc sec of both sides of the equation
2x = sec₋¹(y/9)
Divide both sides by 9
x = 1/2[sec₋¹(y/9)]
Hence, the value of x is x = 1/2[sec₋¹(y/9)]
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22. The expression 3(-4b) - 2(a - b - c) is equal to which of the following expressions?
(1) -2a - 10b - 2c
(2) -2a - 10b + 2c
(3) -2a -5b + 2c
(4) -2a -4b - 2c
(5) 2a-4b - 2c
Answers
Answer:
We can simplify the expression as follows:
3(-4b) - 2(a - b - c) = -12b - 2a + 2b + 2c
Combining like terms, we get:
= -2a - 10b + 2c
Therefore, the expression 3(-4b) - 2(a - b - c) is equal to option (2), -2a - 10b + 2c.
Step-by-step explanation:
Im smart
what would the speed be if the tailwind of an airplane is 150 mph and the headwind remains at 100 mph
Answers
Answer:
To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind.
To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)
To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)
To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)Speed of airplane = 50 mph
To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)Speed of airplane = 50 mphTherefore, the speed of the airplane would be 50 mph.
helpppp
in the figure below, m WXZ=72 degrees, and m 2 is three times m 1. Find m 1
Answers
Answer:
Step-by-step explanation:
If g(x) = 3x -2 and (gof)(x) = 15x + 10, find f(x).
Answers
Answer:
the function f(x) is f(x) = 5x + 4.
Step-by-step explanation:
To find f(x), we need to use the formula:
(gof)(x) = g(f(x)) = 3f(x) - 2
We are given that (gof)(x) = 15x + 10, so we can substitute this expression into the formula to get:
3f(x) - 2 = 15x + 10
Simplifying this equation, we get:
3f(x) = 15x + 12
Dividing both sides by 3, we get:
f(x) = 5x + 4
Therefore, the function f(x) is f(x) = 5x + 4.
The line plot shows the number of televisions
owned by the families in a neighborhood. Use
clusters, gaps, peaks, outliers, symmetry,
skewness, and spread to describe the shape of
the distribution and summarize the data. (Example 1)
●●●+o
...
Number of Televisions
.....
N.
2
.....
●
4
6
8
10
Answers
The correct statements are as follows:-
There is a cluster from 3 to 4.
There is a gap between 1 and 3.
There is a peak at 4.
The data is skewed left.
We have,
Scatter plots are graphs that show how two variables in a data collection relate to one another. On a two-dimensional plane or in a Cartesian system, it represents data points.
The right statements for the dot plots are as follows:-
There is a cluster from 3 to 4.
There is a gap between 1 and 3.
There is a peak at 4.
The data is skewed left.
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Please help me out it’s a new topic and I don’t know how to do it
Answers
Answer:
=x2-100
Step-by-step explanation:
When I said x2 I mean (x*x)
A red marble is drawn from a bag containing 3 red and 3 blue marbles. If the red marble is not replaced, find the probability of drawing a second marble that is blue.
Answers
The probability of drawing a second marble that is blue is 3/5
Finding the probability of drawing a second marble that is blue.From the question, we have the following parameters that can be used in our computation:
A red marble is drawn from a bag containing 3 red and 3 blue marbles.
If the marbles were not replaced, then we have
P(Red) = 3/6
Now there are
3 blue marbles and 2 red marbles left
So, we have
The probability of choosing a blue marble, after a red marble is
P(Blue) = 3/5
Evaluate
P(Blue) = 3/5
Hence, the probability of choosing a blue marble, after a red marble is 3/5
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Element X is a radi
an experiment starts out with 490 grams of Element X, write a function to represent
the mass of the sample after t years, where the monthly rate of change can be found
from a constant in the function. Round all coefficients in the function to four decimal
places. Also, determine the percentage rate of change per month, to the nearest
hundredth of a percent.
Answers
m(t) = 490(1 + r)^(12t)
This function takes into account that there are 12 months in a year, so we need to raise the quantity (1 + r) to the power of 12t to account for the number of months that have passed.
To find the percentage rate of change per month, we can use the following formula:
percentage rate of change per month = r * 100
For example, if r = 0.02, then the function to represent the mass of the sample after t years would be:
m(t) = 490(1 + 0.02)^(12t)
And the percentage rate of change per month would be:
percentage rate of change per month = 0.02 * 100 = 2%
Note that the rate of change could be positive or negative depending on the decay or growth of Element X, but the formula above assumes a positive growth rate.
If tanθ=-5/2 and sinθ>0, find the exact values of sinθ,cosθ,secθ,cscθ,cotθ.
Answers
The exact values are;
sinθ = -5/√29
cosθ = 2/√29
secθ =√29/2
cscθ = -√29/5
cotθ = -2/5
We are given that
tanθ=-5/2 and sinθ>0
First quadrant: I, 0°<θ<90°
We can find the first quadrant between 0° and 90° , the values from 0 to the positive numbers for the x-axis and the y-axis, the functions sine, cosine and tangent will always have positive values.
sinθ = -5/√29
cosθ = 2/√29
secθ =√29/2
cscθ = -√29/5
cotθ = -2/5
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compute (x^2 + 3x - 10) / (x + 5)
Answers
Step-by-step explanation:
[tex] \frac{ {x}^{2} + 3x - 10 }{x + 5} \\ = \frac{(x + 5)(x - 2)}{(x + 5)} \\ = (x - 2)[/tex]
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