The number of minutes when they would both paint the same strip of wood is 8 minutes.
In how many minutes would they paint the same strip of wood?The linear equation that represents the total strip of wood that is painted by Henry is: amount of strips already painted + (strips painted per minute x minute)
14 + (3½x m)
14 + 3½m
The linear equation that represents the total strip of wood that is painted by Sandy is: amount of strips already painted + (strips painted per minute x minute)
10 + (4 x m)
10 + 4m
When both people paint the same strip of wood, the two above equations would be equal.
10 + 4m = 14 + 14 +3½m
4m - 3½m = 14 - 10
0.5m = 4
m = 4 / 0,5 = 8
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how would I solve and what would the answer be?
Given that:
f(x) = |x| and g(x) = x + 6
[tex](f\circ g)(x)=|x+6|[/tex]and
[tex](g\circ f)(x)=|x|+6[/tex]Enrique takes out a student loan to pay for his college tuition this year. Find the interest on the loan if he borrowed $2500 at an annual interest rate of 6% for 3 years.Simple interest
Answer:
$450
Explanation:
The interest of the loan can be calculated using the following equation:
[tex]I=P\cdot r\cdot t[/tex]Where P is the amount that he borrowed, r is the interest rate and t is the number of years.
So, replacing P by 2500, r by 0.06, and t by 3 years, we get:
[tex]\begin{gathered} I=2500^{}\cdot0.06\cdot3 \\ I=450 \end{gathered}[/tex]Then, the interest of the loan is $450.
I need help with this page pls help me !!
N 6
we have
[tex]216=\frac{r}{2}+214[/tex]a ------> subtraction
subtract 214 both sides
[tex]\begin{gathered} 216-214=\frac{r}{2} \\ 2=\frac{r}{2} \end{gathered}[/tex]b ------> multiplication
Multiply by 2 both sides
[tex]\begin{gathered} 2\cdot2=2\cdot\frac{r}{2} \\ r=4 \end{gathered}[/tex]c ------> r=4
For each equation, choose the statement that describes its solution. If applicable, give the solution.
w=2
All real numbers are solutions
1) In this question, let's solve each equation, and then we can check whether there are solutions, which one would be.
2) Let's begin with the first one, top to bottom
[tex]\begin{gathered} 2(w-1)+4w=3(w-1)+7 \\ 2w-2+4w=3w-3+7 \\ 6w-2=3w+4 \\ 6w-3w=4+2 \\ 3w=6 \\ \frac{3w}{3}=\frac{6}{3} \\ w=2 \end{gathered}[/tex]Note that we distributed the factors outside the parenthesis over the terms inside.
So for the first one, we can check w=2
3) Moving on to the 2nd equation, we can state:
[tex]\begin{gathered} 6(y+1)-10=4(y-1)+2y \\ 6y+6-10=4y-4+2y \\ 6y-4y-2y=4-4 \\ 6y-6y=0 \\ 0y=0 \end{gathered}[/tex]So, there are infinite solutions for this equation, or All real numbers are solutions
Which of the following correctly identifies the vertices that lie on the major axis of the conic section shown below? (x - 2) 3-2*) (y+5) = 1 4 9 O A. (2,-2) and (2,-8) O B. (-5,5) and (-5,-1) O C. (5,5) and (-1,-5) O D. (0,-5) and (4,-5)
General equation of an ellipse:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]where (h,k) is the center, and a and b are some constants.
If b² is greater than a², then the y-axis is the major axis.
In this case, the ellipse is defined by the next equation:
[tex]\frac{(x-2)^2}{4}+\frac{(y+5)^2}{9}=1[/tex]This means that:
[tex]\begin{gathered} b^2=9 \\ b=\sqrt[]{9} \\ b=3 \end{gathered}[/tex]And, h = 2, k = -5
The vertices on the major axis are computed as follows:
(h, k+b) and (h, k-b)
Substituting with h = 2, k = -5, and b = 3, the vertices are:
(2, -5+3) and (2, -5-3)
(2, -2) and (2, -8)
What is the area of the figure? Please if you don’t understand ask me to move onto the next tutor as many people have gotten these questions wrong thank you and please double check and take your time!
Determine the area of the figure.
[tex]\begin{gathered} A=3\cdot8+12\cdot9+\frac{1}{2}\cdot4\cdot6 \\ =24+108+12 \\ =144 \end{gathered}[/tex]So answer is 144 yards square.
I am creating a study guide and need step by step explanation for this question please
After other workers taken 1 banana, 2 oranges and 1 pear then total fruits left in the basket
[tex]11[/tex]Now the number of oranges left is 4.
So the probability of picking an orange from the basket is
[tex]\frac{4}{11}[/tex]After she took 1st orange then the number of oranges left 3
So the probability of picking an orange for the 2nd time is
[tex]\frac{3}{10}[/tex]Now the number of oranges left is 2, and the total number of fruits is 9. So the probability of picking third fruit also orange is
[tex]\frac{2}{9}[/tex]Suppose that an airline uses a seat width of 16.2 in. Assume men have hip breadths that are normally distributed with a mean of 14 in. and a standard deviation of 1 in. Complete parts (a) through (c) below.
Given:
population mean (μ) = 14 inches
population standard deviation (σ) = 1 inch
sample size (n) = 126
Find: the probability that a sample mean > 16.2 inches
Solution:
To determine the probability, first, let's convert x = 16.2 to a z-value using the formula below.
[tex]x=\frac{\bar{x}-\mu}{\sigma\div\sqrt{n}}[/tex]Let's plug into the formula above the given information.
[tex]z=\frac{16.2-14}{1\div\sqrt{126}}[/tex]Then, solve.
[tex]z=\frac{2.2}{0.089087}[/tex][tex]z=24.6949[/tex]The equivalent z-value of x = 16.2 is z = 24.6949
Since we are looking for the probability of greater than 16.2 inches, let's find the area under the normal curve to the right of z = 24.6949.
Based on the standard normal distribution table, the area from the center to z = 24.6949 is 0.5
Since we want the area to the right, let's subtract 0.5 from 0.5.
[tex]0.5-0.5=0[/tex]Therefore, the probability that a sample mean of 126 men is greater than 16.2 inches is 0.
Robin Sparkles invests $3,760 in a savingsaccount at her local bank which gives 1.8%simple annual interest. She also invests$2,400 in an online savings account whichgives 5.3% simple annual interest. After fiveyears, which one will have earned moreinterest, and how much more interest will ithave earned, to the nearest dollar?
The formula for determining simple interest is expressed as
I = PRT/100
where
I = interest
P = principal or amount invested
T = time in years
R = interest rate
Considering the amount invested in her local bank,
P = 3760
R = 1.8
T = 5
I = (3760 x 1.8 x 5)/100 = 338.4
Considering the amount invested in online savings,
P = 2400
R = 5.3
T = 5
I = (2400 x 5.3 x 5)/100 = 636
After 5 years, the investment in the online savings account earned more interest.
The difference in interest earned is
636 - 338.4 = $298 to the nearest dollar
It has earned $298 more than the local bank's interest
You borrow 200 from a friend you repay the loan in two weeks and agreed to pay eight dollars for interest what is the annual percentage rate? Round your answer to the nearest 10th of a percent
in which quadrant is the given point located (2,-4)
Answer: 4th Quadrant
Step-by-step explanation:
When plotted, the point (2, -4) lies in the 4th quadrant.
The function gives the cost to manufacture x items. C(x) = 15,000 + 8x - x2 -; X = 20,000 20,000 Find the average cost per unit of manufacturing h more items (i.e., the average rate of change of the total cost) at a production level of x, where x is as indicated a smaller values of h to check your estimates. Round your answers to five decimal places.) h 10 1 Cave 5.99950 5.9995 x Estimate the instantaneous rate of change of the total cost at the given production level x, specifying the units of measurement. c' (20,000) = 6 $/item A Need Help? Read It Watch It
We can replace x=20000 in the function so:
[tex]c(20000)=15000+8(20000)-\frac{20000^2^{}}{20000}[/tex]and we simplify:
[tex]c(20000)=15500[/tex]now h=1 is the cost of one more item so we evaluate for 20001
[tex]\begin{gathered} c(20001)=15000+8(20001)-\frac{20001^2}{20000} \\ c(20001)=195010 \end{gathered}[/tex]So for h=1 will be :
[tex]C=0.599950[/tex]A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 65%pure antifreeze. The company wants to obtain 260 gallons of a mixture that contains 45% pure antifreeze. How many gallons of water and how many gallons of the premium antifreeze solution must be
Answer:
80 gallons of water
180 gallons of premium antifreeze solution.
Explanation:
Let's call X the number of gallons of water and Y the number of gallons of the premium antifreeze solution.
The company wants to obtain 260 gallons of the mixture, so our first equation is:
X + Y = 260
Additionally, the mixture should contain 45% of pure antifreeze and the premium antifreeze solution contains 65% pure antifreeze. So, our second equation is:
0.45(X + Y) = 0.65Y
Now, we need to solve the equations for X and Y. So, we can solve the second equation for X as:
[tex]\begin{gathered} 0.45(X+Y)=0.65Y \\ 0.45X+0.45Y=0.65Y \\ 0.45X=0.65Y-0.45Y \\ 0.45X=0.2Y \\ X=\frac{0.2Y}{0.45} \\ X=\frac{4}{9}Y \end{gathered}[/tex]Then, we can replace X by 4/9Y on the first equation and solve for Y as:
[tex]\begin{gathered} \frac{4}{9}Y+Y=260 \\ \frac{13Y}{9}=260 \\ 13Y=260\cdot9 \\ 13Y=2340 \\ Y=\frac{2340}{13} \\ Y=180 \end{gathered}[/tex]Finally, replacing Y by 180, we get that X is equal to:
[tex]\begin{gathered} X=\frac{4}{9}Y \\ X=\frac{4}{9}\cdot180 \\ X=80 \end{gathered}[/tex]Therefore, the solution should have 80 gallons of water and 180 gallons of premium antifreeze solution.
What is the constant of proportionality of x 0 4 8 12 y 0 3 6 9
Answer:
3/4
Step-by-step explanation:
As y is changing by 3, x is changing by 4
What are the coordinates of point B (3,-2) after a 90° clockwise rotation about the origin?
Ms.Lee has 7 boys and 13 girls in her class. If she selects a student at random, what is the probability that she will select a boy?
Answer: 35 percent chance
Step-by-step explanation: 7+13=20 20x5=100 7x5=35 13x5=65 65+35=100
3/4 divided by 3/5 how do you work the problem
We copy the first number, change the division sign to multiplication, then flip the second fraction
Cancel the three's
If you want to simplify the improper fraction, divide the numerator by the denominator
5/4 = 1 1/4
Division Properties of Exponents HW.
Given the expressions:
[tex]\begin{gathered} \frac{4^5}{4^2} \\ \text{and} \\ \frac{4^2}{4^5} \end{gathered}[/tex]we can use the following property for exponents in quotients:
[tex]\frac{a^n}{a^m}=a^{n-m}[/tex]in this case, we have the following:
[tex]\begin{gathered} \frac{4^5}{4^2}=4^{5-2}=4^3 \\ \text{and} \\ \frac{4^2}{4^5^{}}=4^{2-5}=4^{-3} \end{gathered}[/tex]then, the difference between both expressions is that when they are simplified, they get opposite signs on their exponents.
find the sum to infinity 16,4,1,1/4
Answer:
The sum to infinity of the given series is;
[tex]S_{\infty}=21\frac{1}{3}[/tex]Explanation:
From the given series, we can see that the series is a Geometric Progression (GP) because it has a common ratio;
[tex]\begin{gathered} r=\frac{4}{16}=\frac{1}{4} \\ r=0.25 \end{gathered}[/tex]The formula to calculate the sum to infinity of a GP is;
[tex]\begin{gathered} S_{\infty}=\frac{a}{1-r} \\ \text{For;} \\ 0Where;a = first term = 16
r = common ratio = 0.25.
substituting we have;
[tex]\begin{gathered} S_{\infty}=\frac{16}{1-0.25}=\frac{16}{0.75} \\ S_{\infty}=21\frac{1}{3} \\ S_{\infty}=21.33 \end{gathered}[/tex]Therefore, the sum to infinity of the given series is;
[tex]S_{\infty}=21\frac{1}{3}[/tex]LE Answer two questions about Systems A and B: System A System B 3.7 +12y = 15 x+4y=5 10y = -2 73 - 10y = -2 1) How can we get System B from System A? Choose 1 answer: A Replace one equation with the sum/difference of both equations B Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations C Replace one equation with a multiple of itself D Replace one equation with a multiple of the other equation 2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution? Choose 1 answer: А Yes B No
The first equation from System A is what is called a linear combination of the first equation of System B: the equation are equivalent.
System A equation is equal to the System B equation multiplied by a factor of 3 on both sides, so they contain the same information.
Answer: Yes. The systems are equivalent as their equations are equivalent.
282The number of germs in a sample can be measured by the equation f(x)=15x + 145. Temperature represents the domain of the sample while the range isthe number of germs. If a doctor wants to keep the amount of germs to be less than 300,what is the approximate domain of temperatures to keep the sample under 300?
Answer
The approximate domain temperature is 10
Step-by-step explanation:
Given the following model function
f(x) = 15x + 145
Mathematically
15x + 145 < 300
Collect the like terms
15x < 300 - 145
15x < 155
Divide both sides by 15
15x/15 < 155/15
x < 10.33
Transforming the graph of a function by shrinking or stretching
So,
From the graph of the function f(x), we can notice it contains the points:
[tex]\begin{gathered} f(2)=-4\to(2,-4) \\ f(-2)=-2\to(-2,-2) \end{gathered}[/tex]If we use the transformation, we obtain the new points:
[tex]\begin{gathered} f(\frac{1}{2}x)\to f(\frac{1}{2}(2))=f(1)=-\frac{7}{2}\to(2,-\frac{7}{2}) \\ f(\frac{1}{2}x)\to f(\frac{1}{2}(-2))=f(-1)=-\frac{5}{2}\to(-2,-\frac{5}{2}) \end{gathered}[/tex]All we need to do to graph the new line is to plot the points:
[tex](2,-\frac{7}{2})\text{ and }(-2,-\frac{5}{2})[/tex]And form a line that passes through them.
A number divisible by 2, 5 and 10 if the last digit is _______.
A. An even number
B. O
C. 0 or 5
D. An odd number
Answer :- B) 0
Only a number ending with the digit 0 is divisible by 2,5 and 10
Example :-
20 ÷ 2 = 10
20 ÷ 5 = 4
20 ÷ 10 = 2
Here, 20 is the number that ends with 0.
Help math help math
What is the answer
The ratio 25 : 15 as a fraction in the simplest form can be written as 5/3.
What is ratio?The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. Ratio are represented in the following way - a : b, c : d etc
Given is 25 to 15.
We can express this ratio as a fraction in the simplest form as -
25 : 15 = 25/15
Now, we have to ensure that only whole numbers are their in the numerator and denominator. So in simplest form, we can write -
25 : 15 = 25/15 = (5 x 5)/(5 x 3) = 5/3
Simplest form in fraction will be 5/3
Therefore, the ratio 25 : 15 as a fraction in the simplest form can be written as 5/3.
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Polly surveyed 850 teenagers to find out their favorite type of music she found that 32% of teenagers to Vader like hard rock how many Teenage evade light Hard Rock
The survryed was on 850 teenagers
Number of teenage that evade light hard rock = 32% of 850
=32/100 x850
=272
help meeeeeeeeee pleaseee !!!!!
The composite functions are evaluated and simplified as:
(f o g)(x) = 9x² + 5
(g o f)(x) = 3x² + 15
How to Evaluate a Composite Function?To evaluate a composite function, the inner function is evaluated first using the given input. After then, the output of the inner function is used as the input to evaluate the outer function.
Given the following:
f(x) = x² + 5g(x) = 3xTherefore:
a. (f o g)(x) = f(g(x))
Substitute g(x) for x into f(x) = x² + 5
f(g(x)) = (3x)² + 5
Simplify the function
f(g(x)) = 9x² + 5
b. (g o f)(x) = g(f(x))
Substitute f(x) for x into g(x) = 3x:
g(f(x)) = 3(x² + 5)
Simplify the function
g(f(x)) = 3x² + 15
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The surface area of a cell phone screen is 4900 mm². Use the fact that 10 mm = 1 cm to convert this area to cm². Round your answer to the nearest whole number. Do not type the units in the space below.
Answer:
49 cm²
Step-by-step explanation:
10 mm = 1 cm
1 mm = 1/10 cm
4900 mm² = 4900 × mm × mm
4900 mm² = 4900 × 1/10 cm × 1/10 cm = 49 cm²
15. The new county park is one mile square. What would be the length of a road around its boundaries?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
County park:
area = 1 mile²
Step 02:
length of a road around:
area = side²
1 mile ² = s²
[tex]\begin{gathered} s^2=1 \\ s=\sqrt[]{1}=\text{ 1 } \end{gathered}[/tex]s = 1 mile
perimeter = 4 s = 4 * 1 mile = 4 miles
The answer is:
the length of a road around its boundaries is 4 miles
7x - 15 < 48. Elrich planted seeds from each of x different seed packets in his garden. To plant these seeds, he had to remove plants that were already in the garden. Taking into account the plants he removed and the seeds he planted, he expected to have (select) plants in the garden. From how many different seed packets did Elrich recently plant seeds?
Elrich planted 7 seeds from each of x different seed packets in his garden. To plant these seeds, he had to remove 15 plants. that were already in the garden. Taking into account the plants he removed and the seeds he planted, he expected to have less than equal to 48 plants in the garden.
The inequality :
[tex]7x-15\leq48[/tex]Simplify for x:
[tex]7x-15\leq48[/tex]
11. (04.02 LC) Saving all the money in a safe at home most likely means (5 points) being stingy being dishonest being untrusting O being thrifty
Saving all the money in a safe at home most likely means D. being thrifty
What is money?Money is any commodity or verifiable record that is widely accepted in a given country or socioeconomic environment as payment for products and services and repayment of debts, such as taxes.
Money enables us to meet our most basic requirements, such as purchasing food and shelter and paying for healthcare. Meeting these demands is critical, and if we don't have enough money to do so, our personal well-being and the community's overall well-being suffer considerably.
In this case, saving the money means that the person is careful with spending and doesn't want to waste the money. This implies thrifty.
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Answer:
Being thrifty