The area formula of a circle is :
[tex]A=\frac{1}{4}\pi D^2[/tex]From the problem, the diameter is 8 inches.
The area will be :
[tex]\begin{gathered} A=\frac{1}{4}\pi(8)^2 \\ A=50.27 \end{gathered}[/tex]The answer is 50.27 in^2
I am unsure how to set this problem up so I can begin solving, can you please assist me?
Since it is a right triangle, we can apply trigonometric functions:
Sin a = opposite side / hypotenuse
Where:
a = angle = 25°
Opposite side = x
Hypotenuse = 30
Replacing:
Sin 25 = x / 30
Solve for x :
Sin 25 (30) = x
x = 12.68
You invest $1,000 in each of two accounts. Account A earns simple interest at a rate of 2.42% over 4 years. Account B earns simple interest at a rate of 2.42% over 24 months. Find the interest earned by each account. How does the interest earned by the two accounts compare?
ANSWER
Account A = $96.80
Account B = $48.40
EXPLANATION
We have that in the two accounts A and B, $1000 is invested.
We want to find the simple interest earned by the two accounts. To do this, we apply the formula for Simple Interest:
[tex]SI=\frac{P\cdot R\cdot T}{100}[/tex]where P = principal (amount invested)
R = rate
T = amount of time
ACCOUNT A
It earns simple interest at a rate of 2.42% over 4 years.
Therefore, the simple interest earned is:
[tex]\begin{gathered} SI=\frac{1000\cdot2.42\cdot4}{100} \\ SI=\text{ \$96.8}0 \end{gathered}[/tex]ACCOUNT B
It earns simple interest at a rate of 2.42% over 24 months. For this, we have to divide by 12 months (since the formula is originally for year).
Therefore, the simple interest earned is:
[tex]\begin{gathered} SI=\frac{1000\cdot2.42\cdot24}{100\cdot12} \\ SI=\text{ \$48.40} \end{gathered}[/tex]We have calculated the Simple Interest for both accounts.
We see that the simple interest for Account A is twice that of Account B. This is simply because Account A earned for twice the amount of time that Account B earned for.
help meeee please !!
thank you
Answer:
i'm wath
Step-by-step explanation:
in whatwhat because wich
the price of a t-shirt is $20, but you have a coupon that lowers the price by 10%. What is the price of the t-shirt after using the coupon?a.$2b.$10c.$18d.$20
ANSWER
[tex]C\text{. }\$18[/tex]EXPLANATION
To find the price of the t-shirt after using the coupon, find 10% of the price of the shirt and subtract that from the price of the shirt.
10% of the price is:
[tex]\begin{gathered} \frac{10}{100}*20 \\ \\ \$2 \end{gathered}[/tex]Now, subtract that from the price of the shirt. That is:
[tex]\begin{gathered} \$20-\$2 \\ \\ \Rightarrow\$18 \end{gathered}[/tex]That is the price of the shirt after the coupon is used. The answer is option C.
Mrs. Taylor caught 6 bats in her attic in 12
minutes. How long would it take to catch 5 bats?
Estimate the sum or difference 9.84-1.86
Answer: The estimated sum or difference would be 8.00. If not estimated it would be 7.98.
Step-by-step explanation:
If we differentiate the given numbers from 9.84-1.86, the answer will be 7.98 exactly.
As 7.98 is closer to 8.00, we can easily estimate the number to be 8.00.
3 4. Dan bought soda for his family's party. He bought 3 1/2 liters of Pepsi and 5 3/4 liters of Sprite. They drank all but 2 3/8 liters of soda. How much soda did Dan-and his family drink?
The total amount of soda is
[tex]3\frac{1}{2}+5\frac{3}{4}[/tex]In order to make this addition, we must convert these fractions into a simple fraction form. That is,
[tex]\begin{gathered} 3\frac{1}{2}=\frac{2\cdot3+1}{2}=\frac{7}{2} \\ \text{and} \\ 5\frac{3}{4}=\frac{4\cdot5+3}{4}=\frac{23}{4} \end{gathered}[/tex]so, the total amount of soda is given by
[tex]\frac{7}{2}+\frac{23}{4}[/tex]which gives
[tex]\begin{gathered} \frac{7}{2}+\frac{23}{4}=\frac{14}{4}+\frac{23}{4}=\frac{14+23}{4}=\frac{37}{4} \\ \end{gathered}[/tex]Now, we must subtact 2 3/8 of soda and we must convert it into a simple fraction form:
[tex]2\frac{3}{8}=\frac{8\cdot2+3}{8}=\frac{19}{8}[/tex]Then, Dan's family drank:
[tex]\frac{37}{4}-\frac{19}{8}[/tex]which gives
[tex]\frac{37}{4}-\frac{19}{8}=\frac{74}{8}-\frac{19}{8}=\frac{55}{8}[/tex]that is, they drank 55/8 of soda. In mixed fraction form, this result is equivalent to
[tex]\frac{55}{8}=6\frac{7}{8}[/tex]1+1dynzg sfbstjstjstjj
equation
[tex]\frac{2342424}{456546456}+\sqrt[34535345]{4r3535}-\sin 453\sin ^{-1}43535\cos ^{-1}5345678^{76867}\int ^{\infty}_086\int 6878\sqrt[7686786]{78767\text{ }e^{655757\begin{cases}x=75665 \\ y=5345346363\gamma\end{cases}}}[/tex]what is the coordinate of the midpoint of KL write your answer as an integer or a decimal or mixed number in simplest form
(-14.5, 0)
Explanations:
The formula for finding the midpoint of two coordinates is expressed as;
[tex]m(x,y)=(\frac{x_{1+}x_2}{2},\frac{y_1+y_2}{2})[/tex]For the given coordinates of K and L, since there is no y-axis, hence:
K = (-16, 0)
L = (-13, 0)
Get the midpoint of KL;
[tex]\begin{gathered} m_{kl}=(\frac{-16+(-13)}{2},\frac{0+0}{2}) \\ m_{kl}=(\frac{-16-13}{2},\frac{0}{2}) \\ m_{kl}=(-\frac{29}{2},0) \\ m_{kl}=(-14.5,0) \end{gathered}[/tex]Hence the midpoint of KL will be at (-14.5, 0)
Use the distributive property to simplify the expression:
3(2p+5)-10
PLEASE HELP ASAP I'LL GIVE 100 POINTS AND BRAINY IF YOU CAN HELP ME!!!!!!!!!!!!
Answer:
6p+5
Step-by-step explanation:
3(2p+5)−10
Use the distributive property to multiply 3 by 2p+5.
6p+15−10
Subtract 10 from 15 to get 5.
6p+5
Hello my child needs help with this problem can you please help meKyle has a storage box that is 2 ft. long, 3 ft. high, and has a volume of 12 ft. 3 . Myla has a storage box that is 4 ft. high, 2 ft. long, and has a volume of 16 ft. 3. What are the widths of Kyle and Myla's boxes? Explain how you know.
SOLUTION:
Case: Volumes
[tex]\begin{gathered} Volume \\ V=l\times w\times h \end{gathered}[/tex]Where l is length, w is width and h is height.
Given:
Kyle has a storage box that is 2 ft. long, 3 ft. high, and has a volume of 12 ft. 3
Myla has a storage box that is 4 ft. high, 2 ft. long, and has a volume of 16 ft. 3
Method:
For Kyle,
Volume:
[tex]\begin{gathered} V=l\times w\times h \\ 12=2\times w\times3 \\ 12=6w \\ w=\frac{12}{6} \\ w=2ft \end{gathered}[/tex]For Myla,
Volume:
[tex]\begin{gathered} V=l\times w\times h \\ 16=2\times w\times4 \\ 16=8w \\ w=\frac{16}{8} \\ w=2ft \end{gathered}[/tex]The length and width of both boxes are 2ft and 2ft respectively. But they have different heights.
Final answer:
Both have a width of 2ft
Explanation: Same length and width, different heights hence different width
the graph y = sin x(dashed line) has been translated to give graph G
The equation of the translated function G(x) is given by:
G(x) = sin(x) + 2.
What is a translation?There are many transformations that can happen to the graph of a function, such as translation, stretch, compression, rotation, reflection, dilation and so on.
In the context of this problem, the transformation was a translation, in which the graph of the function is moved either left, right, up or down.
The parent function in this problem is:
y = sin(x).
From the given image, the function y, given by the dashed line, was shifted up 2 units to generate the function g(x), hence the definition of function g(x) is given by:
g(x) = sin(x) + 2.
The addition by 2 in the range of the function represents the translation up 2 units of the function.
What is the missing information?The graph is missing and is given by the image at the end of the answer.
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write the quotient in the standard form a+bi.9/3-i
I am doing calculus and I am supposed to use the tips it gives us and write it step by step and get explain each step. I can not use L hospitals rule, but I don’t know where to start
The value is 1
From the question, we have
lim_(K→0) ((sin(AK))^2)/((sin(BK))^2 )
Differentiate the above form, we get
=lim_(K→0) ((2cos(AK)))/((2cos(BK)) ) (Applying l hospital rule)
Now substitute the limit,
=2/2 = 1
L’Hospital’s Rule :
An input value that a function approaches and yields some result is referred to as a limit. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity. A general technique for assessing indeterminate forms like 0/0 or / is the L'Hospital rule. L'Hospital's rule is applied to calculate the limits of indeterminate forms for calculus derivatives. It is possible to use the L Hospital rule many times. This rule is still valid after being applied, and it will take any indefinite form. L'Hospital's Rule cannot be applied if the issue is not of the indeterminate types.
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I need help solving this practice, I will send an additional picture of the actual problem itself
The multiplicities of the zeros are how many times that factor appeared in the factored form of a polynomial function.
If the multiplicities are even, then they are tangent to the x-axis
So, the graph is tangent to x at -6
If the multiplicities are odd, then they cross while hugging the x-axis.
So, the graph of the function crosses while hugging the X-axis at 1
And the graph crosses through at the values with no multiplicities, which are 0 and 4
So, the answers are:
a) Is tangent to
b) Crosses straight through
C) Crosses through whle hugging
d) Crosses straight through
write your answer in exponential form. 8^5 multiply 8^-2
Answer: 8^3
Explanation:
We want to multiply 8^5 multiply 8^-2
We would apply the rule of exponent;
a^b * a^c = a^(b + c)
By comparing both expressions,
a = 8
b = 5
c = - 2
Thus, we have
8^5 * 8^-2 = 8^(5 + - 2) = 8^(5 - 2)
= 8^3
Flo measures the amount of water her high pressure sprayer uses and finds that it uses 20 gallons of water in 4 minutes and 30 gallons in 6 minutes. Complete the table, Then describe whether it makes sense to use a constant rate to describe the relationship . Explain I need help I’m confused
Given, 20 gallons per 4 minutes, let's find the unit rate:
[tex]\frac{20}{4}=5\frac{\text{gal}}{\min }[/tex]Also, given 30 gallons per 6 minutes, that also has an unit rate of:
[tex]\frac{30}{6}=5\frac{\text{gal}}{\min }[/tex]Thus, the constant of proportionality is 5.
Let's complete the table:
Yes, it does make sense. Because a high pressure sprayer should ideally be using a constant rate of water.
Two angles are supplementary if the sum of their measures is 18
Let:
x = 1st angle
y = 2nd angle
Since they are supplementary:
[tex]x+y=180_{\text{ }}(1)[/tex]One is 54 more than 1/2 of the other, so:
[tex]y=\frac{1}{2}x+54_{\text{ }}(2)[/tex]Replace (2) into (1):
[tex]\begin{gathered} x+\frac{1}{2}x+54=180 \\ \frac{3}{2}x=180-54 \\ \frac{3}{2}x=126 \\ x=\frac{2}{3}\cdot126 \\ x=84 \end{gathered}[/tex]Replace x into (2):
[tex]\begin{gathered} y=\frac{1}{2}(84)+54 \\ y=42+54 \\ y=96 \end{gathered}[/tex]Answer:
The two angles are 84⁰ and 96⁰
Hello it’s a 4 part question I just need help however I can only post one picture at a time
Answer:
Part a:
0% 3000
5% 3646.51
10% 5247.02
20% 6220.8
Explanation:
Part a:
We need to evaluate the function in the r values given:
If the rate is 0% then r = 0
[tex]S=3000(1+0)^4=3000[/tex]If the rate is 5%, then r = 0.05
[tex]S=3,000(1+0.05)^4\approx3646.51[/tex]If the rate is 10%, then r = 0.1
[tex]S=3,000(1+0.1)^4=4392.3[/tex]If the rate is 15%, then r = 0.15
[tex]S=3,000(1+0.15)^4=5247.02[/tex]If the rate is 20%, then r = 0.2
[tex]S=3,000(1+0.2)^4=6220.8[/tex]Order the following math expressions from least to greatest. 100 = 22 = 02 = = 32
First, we need to simplify the expressions, as follows:
[tex]\begin{gathered} \sqrt[]{100}=10 \\ \sqrt[]{9}=3 \\ 2^2=4 \\ \sqrt[]{4}=2 \\ -4^2=-16 \\ 0^2=0 \\ \sqrt[]{1}=1 \\ 3^2=9 \\ (-4)^2=16 \end{gathered}[/tex]Then, the ordered list is:
[tex]\begin{gathered} -16,0,1,2,3,4,9,10,16 \\ or \\ -4^2,0^2,\sqrt[]{1},\sqrt[]{4},\sqrt[]{9},2^2,3^2,\sqrt[]{100},(-4)^2 \end{gathered}[/tex]URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
How would we find the value of x?
4. Which expression represents the area of arectangle where the length is 9 and thewidth is 3x - 8.A. 27x - 8B. 24x - 16C. 27x - 72D. 12x - 8
Area of a rectangle = length x width
A = 9 (3x-8)
A = 9(3x) + 9(-8)
A= 27x - 72
Please help!! What is the solution if the equation below
The answer to the given equation question is Option C - 2
What does square root mean ?A square root of a number x is a number y such that y2 = x; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x.[1] For example, 4 and −4 are square roots of 16, because 4^2 = (−4)^2 = 16.
Given : [tex]\frac{\sqrt{2x} }{\sqrt{x-1} }[/tex] = 2
On taking square roots on both sides we get :
=> [tex]\frac{2x}{x-1}[/tex] = 2
On cross multiplying
=> 2x = 2x - 2
After the calculations we get the solution as 2
Thus the correct answer is option c - 2 .
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Given: - 7(x + 2) + 4x = 6(2x - 4) Prove: x = 2/3
Answer:
2/3 = x
Step-by-step explanation:
- 7 ( x + 2 ) + 4x = 6 ( 2x - 4 )
First, solve the brackets.
-7x - 14 + 4x = 12x - 24
Combine like terms.
-3x - 14 = 12x - 24
Add 3x to both sides.
-14 = 12x + 3x - 24
-14 = 15x - 24
Add 24 to both sides.
-14 + 24 = 15x
10 = 15x
Divide both sides by 15.
10/15 = x
To simplify the answer divide numerator and denominator by 5.
2/3 = x
What is 3/5 divided 2/3
When dividing two fractions that is 3/5 by 2/3 then we get the answer as 9/10 = 0.9.
Explanation:Steps to divide fractions:
The first step in dividing fractions is to find the reciprocal of the second fraction (reverse the numerator and denominator). Then, multiply the numerators. Then multiply the two denominators together. Finally, if necessary, simplify the fractions.Given two fractions 3/5 and 2/3,
to find 3/5 divided by 2/3 then,
Determine the reciprocal of the fraction 2/3:3/2 is the reciprocal of fraction 2/3.
The equivalent fraction for 3/5 divided by 2/3 is obtained by multiplying 3/5 by the reciprocal of 2/3.
= 3/5 x 3/2
= 9/10
= 0.9
Hence,
As a fraction, 3/5 divided by 2/3 equals 9/10 = 0.9
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Graph the circle x^2+y^2=9
Given:
A circle with the equation:
[tex]x^2+y^2\text{ = 9}[/tex]Solution
Recall that the general equation of a circle is of the form:
[tex](x-a)^2+(y-b)^2=r^2[/tex]Where (a, b) are coordinates of the center and r is the radius of the circle.
Re-writing the given equation using the general form gives us:
[tex](x-0)^2+(y-0)^2=3^2[/tex]Hence, the center and radius of the circle are (0, 0) and 3 respectively.
The graph of the equation is shown below:
The graph is obtained by first locating the center of the circle (0,0) on the graph. Then, we measure 3 units from the center to construct the required circle.
You’re getting ready to fill up your halloween candy jar that weighs 2.5 pounds when empty. On Halloween night you only go out in the neighborhoods who give out the large sized candy bars. Each large candy bar you collect weighs 0.5 pounds
The number of times that the candy jar is more than that of the neighborhood is 5 times.
How to illustrate the information?From the information, the candy jar weighs 2.5 pounds when empty. and when you only go out in the neighborhoods who give out the large sized candy bars that weighs 0.5 pounds.
The number of times that yours is higher will be the weight of candy bar that you have divided by the weight of that of your neighborhood
= You candy weight / Neighborhood weight
= 2.5 / 0.5
= 5
Yours is 5 times more. This illustrates the concept of division.
The complete question is written below.
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You’re getting ready to fill up your halloween candy jar that weighs 2.5 pounds when empty. On Halloween night you only go out in the neighborhoods who give out the large sized candy bars. Each large candy bar you collect weighs 0.5 pounds. How many times is your candy jar more than that of the. neighborhood?
12 eggs for3 dollars how much does per egg cost
Start of QuestionsCompound Interest: Suppose $1,100 is invested in a savings account that pays 3% compounded semiannually, how much is in the account at the end of 1 1/2 years?There is $ ? in the account after 1 1/2 years.
Explanation:
The amount in the account can be calculated as:
[tex]A=P(1+r)^t_{}[/tex]Where P is the initial amount, r is the interest rate and t is the number of times the interest is compound. In 1 1/2 years, the interest is compound 3 times because it is compound every 6 months.
Then, replacing P by 1,100, r by 3% = 0.03 and t by 3, we get:
[tex]\begin{gathered} A=1100(1+0.03)^3 \\ A=1100(1.03)^3 \\ A=1100(1.0927) \\ A=1201.99 \end{gathered}[/tex]therefore, there is $1202 in the account after 1 1/2 years.
Jayson buys a car and pays by installments. Each installment is $567 per month. After 48 months Jayson owes $1,250. What was the total price of the vehicle?
10 points
use an area model and standerd multiplecation!
The total price of the vehicle to Jayson is $28,466 since he has paid $567 for 48 months and still owes $1,250.
How is the total price determined?We can use the mathematical operations of multiplication and addition to compute the car's total price.
Installment payment per month = $567
The total installments paid for 48 months = $27,216 ($567 x 48)
The amount Jayson still owes = $1,250
Total price = $28,466 ($27,216 + $1,250)
Thus, Jayson would pay a total price of $28,466 for the vehicle.
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