Total fee = $75
Number of months = 3
Divide the total fee by the number of months
75/3 = $25 per month
Find the exact value of sin A and cos A where a = 9 and b = 10 and
Given data:
a=9 , b = 10
use the phythagoras theorem,
[tex]c=\sqrt[]{a^2+b}^2[/tex][tex]\begin{gathered} c=\sqrt[]{9^2+10^2} \\ c=\sqrt[]{81+100} \\ =\sqrt[]{181} \end{gathered}[/tex]thus,
[tex]\sin A=\frac{opp}{\text{hypo}}[/tex][tex]\text{sinA}=\frac{9}{\sqrt[]{181}}[/tex]and,
[tex]undefined[/tex]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.
A spinner has the sections A through F. The spinner is spun and a 6-sided die is rolled. What is the probability that the outcome will be D and 5?1/361/181/121/6
To find the probability of having a D and %, we would use the concept of mutually exclusive events here
But probability is given as
[tex]P=\frac{\text{ number of favourable outcomes}}{\text{total number of }possible\text{ outcomes}}[/tex]The probability of choosing a D is
A, B, C, D, E and F. This can be found as
[tex]P_a=\frac{1}{6}[/tex]The probabilty of choosing a 5 out of 6 possible outcomes is
[tex]P_n=\frac{1}{6}[/tex]The probability of having a D and 5 would be
[tex]\begin{gathered} P=P_a\times P_n \\ P=\frac{1}{6}\times\frac{1}{6} \\ P=\frac{1}{36} \end{gathered}[/tex]From the calculations above, the answer to this question is 1/36
y - 7.8= 5.5 I got 2.9 but I want to be sure I understand and took the right steps
Given the equation:
[tex]y-7.8=5.5[/tex]You need to solve for "y" in order to find its value. In this case, you need to apply the Addition Property of Equality, which states that, if:
[tex]a=b[/tex]Then:
[tex]a+c=b+c[/tex]Therefore, you need to add 7.8 to both sides of the equation in order to solve for "y":
[tex]\begin{gathered} y-7.8+(7.8)=5.5+(7.8) \\ y=13.3 \end{gathered}[/tex]Hence, the answer is:
[tex]y=13.3[/tex]1.5 part 1 question 36 determine whether the graph represent a function explain your answer
Recall that for a graph to correspond to a graph it must pass the vertical line test. The vertical line test consists of drawing vertical lines and if two points of the graph are on the same vertical line then the graph does not represent a function.
Notice the following:
From the above graph, we get that points A B, and C are on the same vertical line, and the same happens for e and f, and m and n. Therefore the graph fails the vertical line test.
Answer: The graph does not represent a function.
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
How do I find the selling price if a store pays 3$ for a magazine. The markup is 5%
We need to find the selling price of a magazine. We know that the store pays $3 for it, and the markup is 5%.
So, we need to add 5% of the initial price to that initial price.
First, let's find:
[tex]5\%\text{ of }\$3=5\%\cdot\$3=\frac{5}{100}\cdot\$3=\frac{\$15}{100}=\$0.15[/tex]Now, adding the previous result to the initial price, we obtain:
[tex]\$3+\$0.15=\$3.15[/tex]Therefore, the selling price is $3.15.
What are the coordinates of the point on the directed line segment from (3,-3) to (7,5) thar oartitions the segment into a ratio of 5 to 3?
Answer:
(x, y) = (5.5, 2)
Explanation:
The coordinates of a point that divide the segment from point (x1, y1) to (x2, y2) into a ratio of a:b can be found using the following equations:
[tex]\begin{gathered} x=x_1+\frac{a}{a+b}(x_2-x_1) \\ y=y_1+\frac{a}{a+b}(y_2-y_1) \end{gathered}[/tex]So, replacing (x1, y1) by (3, -3), (x2, y2) by (7, 5) and the ratio a:b by 5:3, we get that the coordinates of the point are:
[tex]\begin{gathered} x=3+\frac{5}{5+3}(7-3) \\ x=3+\frac{5}{8}(4) \\ x=3+2.5=5.5 \\ y=-3+\frac{5}{5+3}(5-(-3)) \\ y=-3+\frac{5}{8}(5+3) \\ y=-3+\frac{5}{8}(8) \\ y=-3+5=2 \end{gathered}[/tex]Therefore, the coordinates of the point are (x, y) = (5.5, 2)
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
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.
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)
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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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
Trini Cars break down on the highway.show me estimates that she is 20 to 30 miles from the nearest car repair shop she calls a towing company that charges a fee of $80 plus $3 per mile to tow a car.if training uses this towing company, which is the best estimate for the amount of money,m,she will pay for the company to tow her car.a .103 greater than sign and greater than sign 113 b.140 greater than sign M greater than sign 150 c.114 greater than 5 m greater than 170 d. 560 greater than 10 m > 70
We have that the cost is $80 plus $3 per mile, and also we now that the car is 20 to 30 miles from the car repair shop. So we have that Trini have to pay
[tex]\begin{gathered} 80\text{ + 3(20) }\leq\text{ M }\leq\text{ 80 + 3(30)} \\ 80\text{ + 60 }\leq\text{ M }\leq\text{ 80 + 90} \\ 140\text{ }\leq\text{ M }\leq170 \end{gathered}[/tex]So the answer is: b.140 greater than sign M greater than sign 150.
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
In a right triangle, if the hypotenuse is equal to 16 feet and the side adjacent to ∠θ is equal to 5 feet, what is the approximate measurement of ∠θ?
We have the diagram:
We use the trigonometric identity cosine:
[tex]\cos\theta=\frac{adjacent}{hypotenuse}[/tex]Substitute the values:
[tex]\begin{gathered} \cos\theta=\frac{5}{16} \\ \theta=\cos^{-1}(\frac{5}{16})=71.79 \end{gathered}[/tex]Answer: 71.79°
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 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.
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.
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]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]
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
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.
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
What are the coordinates of point B (3,-2) after a 90° clockwise rotation about the origin?
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
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.
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
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.
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]