9514 1404 393
Answer:
B. 16:49
Step-by-step explanation:
The area ratio is the square of the edge length ratio:
area ratio = (4:7)² = 4²:7² = 16:49
_____
It might help you to recall that area is the product of two linear dimensions if each is multiplied by 4/7, the resulting product will be multiplied by (4/7)².
A = LW
A' = (4/7L)(4/7W) = (4/7)²(LW) = (16/49)·A
What is the solution to the equation?
^5 / x+7= -2 (A.) -39 (B.) -17 (C.) 25 (D.) no solution
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {A. \:-39}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \sqrt[5]{x + 7} = - 2[/tex]
➺[tex] \: x + 7 =( { - 2})^{5} [/tex]
➺[tex] \: x + 7 = ( - 2 \times - 2 \times - 2 \times - 2 \times - 2)[/tex]
➺[tex] \: x + 7 = - 32[/tex]
➺[tex] \: x = - 32 - 7[/tex]
➺[tex] \: x = - 39[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
[tex] \sqrt[5]{x + 7} = - 2 \\\\ ➼ \: \sqrt[5]{ - 39 + 7} = - 2 \\ \\➼ \: \sqrt[5]{ - 32} = - 2 \\\\ ➼ \: \sqrt[5]{ - 2 \times - 2 \times - 2 \times - 2 \times - 2} = - 2\\ \\ ➼ \: \sqrt[5]{( { - 2})^{5} } = - 2\\ \\ ➼ \: - 2 = - 2 \\\\ ➼ \: L.H.S.=R. H. S[/tex]
Hence verified.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning. }}{\orange{❦}}}}}[/tex]
The solution of the given equation would be; x = -39.
What is the solution for an equation?The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
WE have been given an equation as,
[tex]\sqrt[5]{x+7} = -2[/tex]
WE need to find the solution of the given equation which can be calculated as;
[tex]\sqrt[5]{x+7} = -2[/tex]
First raise both sides to the power 5;
[tex](\sqrt[5]{x+7} )^5= -2^5[/tex]
Now x + 7 = - 32
subtract 7 from both sides, we get;
x = - 39
Hence, the solution of the given equation would be; x = -39.
Learn more about solving equations here:
https://brainly.com/question/13072448
#SPJ2
Find the value of x to the nearest tenth
Answer:
a^2+b^2=c^2
6^2+6^2=72
square root of 72
=8.49(3sf)
c^2-b^2=a^2
=3
x=3
answer : 3
step by step:
this may seem hard but it is easy.
the first thing to do is to look at the bottom of the shape it shows a right triangle that is missing the hypotenuse lets see how to solve for that:
name the hypotenuse x
then write the equation
x^2= 6^2 + 6^2
x^2= 72
take both the square root of them
x = 8.5
next part is the rectangle and we see that it has been split into 2 right triangles which are the same but the cool part is that if we solve for one of the triangles we solve for the other we are going to do the same steps again notice now we are solving for the right angle that's not labeled if we solve that then that means we solve for the other triangle that is labelled x
first off we know that the hypotenuse is 9 and one angle is 8.5 so here is the equation:
x^2 = 9^2 - 8.5^2
x^2 = 8.75
take square root of both
x = 3
The pH scale measures how acidic or basic a substance is. Lemon juice is said to have a pH of less than 4 and greater than 1.5. Model the normal range of pH values of lemon juice, using a compound inequality.
1.5 > x > 4
1.5 < x < 4
1.5 ≤ x ≤ 4
1.5 ≥ x ≥ 4
Answer: 1.5 < x < 4
Step-by-step explanation:
One day a store sold 36 sweatshirts. White ones cost $10.95 and yellow ones cost $11.50. In all, $404.65 worth of sweatshirts were sold. How many of each color were sold?
The store sold ____ white sweatshirts
Answer:
17 white sweatshirts were sold and 19 yellow sweatshirts were sold.
Step-by-step explanation:
Let w represent the number of white sweatshirts sold and y represent the number of yellow sweatshirts sold.
We can write a system of equations to represent the situation.
Since the store sold a total of 36 sweatshirts, the sum of the white and yellow sweatshirts must total 36. So:
[tex]y+w=36[/tex]
And since each white sweatshirt cost $10.95 and each yellow sweatshirt cost $11.50 and the total profit was $404.65:
[tex]10.95w+11.5y=404.65[/tex]
Solve the system. I'll use substitution this time (though elimination will work just as perfect). From the first equation, subtract w from both sides:
[tex]y=36-w[/tex]
Substitute this into the second:
[tex]10.95w+11.5(36-w)=404.65[/tex]
Distribute:
[tex]10.95w+414-11.5w=404.65[/tex]
Simplify:
[tex]-0.55w=-9.35[/tex]
Divide both sides by -0.55:
[tex]w=17[/tex]
So, 17 white sweatshirts were sold.
Using the modified equation, substitute:
[tex]y=36-(17)=19[/tex]
Therefore, 17 white sweatshirts were sold and 19 yellow sweatshirts were sold.
PLZ HELP !!!
Solve for X
A) 6
B) 5
C) 4
D) 7
use the diagram below to find all missing angles
Answer:
Step-by-step explanation:
Soooo, angle 1 is 157 degrees
That means:
Angle 2 is 23 degrees Supplementary Angles
Angle 3 is 157 degrees Vertical Angle to Angle 1
Angle 4 is 23 degrees Vertical angle to Angle 2
Answers:
angle 2 = 23 degreesangle 3 = 157 degreesangle 4 = 23 degrees=======================================================
Explanation:
Angles 1 and 2 are supplementary as they form a straight line. So the angles add to 180
(angle1)+(angle2) = 180
angle2 = 180-(angle1)
angle2 = 180-157
angle2 = 23 degrees
Angle 4 is congruent to this because angles 2 and 4 are vertical angles. Vertical angles are always congruent. Note how angles 1 and 4 are supplementary.
Since angles 1 and 3 are the other pair of vertical angles, this must mean angle 3 is 157 degrees.
Ms.Peralta's friend Mike is a construction worker. Mike gets paid $15 an hour. After working 9 hours he gets paid 1.25 times his hourly rate. Below you can find Mike's hours for last Friday. - Mike worked for 5 hours - took an 1 hr and 15 minute break for lunch (does not count toward his work hours) - worked for an additional 7.5 hours How much money did Mike make last Friday?
Answer:
Mike made $ 200.63 last Friday.
Step-by-step explanation:
Since Ms. Peralta's friend Mike is a construction worker who gets paid $ 15 an hour, and after working 9 hours he gets paid 1.25 times his hourly rate, and last Friday Mike worked for 5 hours - took an 1 hr and 15 minute break for lunch (does not count toward his work hours) - and worked for an additional 7.5 hours, to determine how much money did Mike make last Friday the following calculation must be performed:
5 + 7.5 = 12.5
12.5 - 9 = 3.5
9 x 15 + (3.5 x (15 x 1.25)) = X
135 + 3.5 x 18.75 = X
135 + 65.625 = X
200.63 = X
Therefore, Mike made $ 200.63 last Friday.
The table shows the results of an experiment in which the spinner shown above was spun 50 times. Find the experimental probability of each outcome.
not shaded
Answer:
[tex]P(x < 4) = \frac{9}{50}[/tex]
Step-by-step explanation:
Given
[tex]n(S) = 50[/tex]
See attachment for distribution
Required
[tex]P(x < 4)[/tex]
This is calculated as:
[tex]P(x < 4) = \frac{n(1) + n(2) + n(3)}{n(S)}[/tex]
Using the data on the frequency distribution table, we have:
[tex]P(x < 4) = \frac{4 + 2 + 3}{50}[/tex]
[tex]P(x < 4) = \frac{9}{50}[/tex]
A small country emits 50,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by 1.1% per year for the next 6 years. In the first year of the agreement, the country will keep its emissions at 50,000 kilotons and the emissions will decrease 1.1% in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the 6 year period, to the nearest whole number?
Answer:
291870 kilotons
Step-by-step explanation:
Since the country cuts its carbon content by 1.1% each year. The initial value at the first year is 50000. Therefore this can be represented by the exponential function:
y = a(b)ˣ ⁻ ¹
where y is the amount of carbon emission in kilotons in x years.
a = 50000, b = 100% - 1.1% = 98.9% = 0.989
y = 50000(0.989)ˣ ⁻ ¹
In the first year: y = 50000(0.989)¹ ⁻ ¹ = 50000
In the second year: y = 50000(0.989)² ⁻ ¹ = 49450
In the third year: y = 50000(0.989)³ ⁻ ¹ = 48906
In the fourth year: y = 50000(0.989)⁴ ⁻ ¹ = 48368
In the fifth year: y = 50000(0.989)⁵ ⁻ ¹ = 47836
In the sixth year: y = 50000(0.989)¹ ⁻ ¹ = 47310
The total emission in 6 years = 50000 + 49450 + 48906 + 48368 + 47836 + 47310 = 291870 kilotons
given the image below which segments are congruent
Answer:
-2+6=4
0+6=6
4+6=10
x+2=2. x=2-2. x=0
Step-by-step explanation:
hope this is helpful
Find the volume of the prism.
Is this correct? I just started learning negative numbers.
Answer:
It's on the negative side, so make sure you put -2.25. But yes, it's right.
In a sample of 230 teenagers, 202 would like to have smaller class sizes at their school. Find the sample
proportion, the margin of error, and the interval likely to contain the true population proportion. If
necessary, round your answers to the nearest percent.
Answer:
The sample proportion is 0.88.
The margin of error is of 0.04.
The interval likely to contain the true population proportion is (0.84,0.92).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Margin of error:
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Sample of 230 teenagers, 202 would like to have smaller class sizes at their school.
This means that [tex]n = 230[/tex], and that the sample proportion is:
[tex]\pi = \frac{202}{230} = 0.88[/tex]
The sample proportion is 0.88.
Standard 95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Margin of error:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.88*0.12}{230}}[/tex]
[tex]M = 0.04[/tex]
The margin of error is of 0.04.
Confidence interval:
Sample proportion plus/minus margin of error. So
0.88 - 0.04 = 0.84
0.88 + 0.04 = 0.92
The interval likely to contain the true population proportion is (0.84,0.92).
400 is 100 times as much as
at 90kph, how far do you travel in 6 hours
Answer:
540 km
Step-by-step explanation:
You find distance by multiplying rate and time. Rate is 90, and time is 6. 90 x 6 = 540 km
Please answer step by step
[tex]27 {x}^{6} {y}^{9} [/tex]
Hope it helps you...
4x(a-b)+3(b-a) factorise
Answer:
-(a-b) (3-4x). hope this helps
How long would it take to fill up 480cm3 pool at 25litres a min
Answer:
the answer is 8cm i think
If the length of EG is 22, find the length of a EQ
Answer:
A. 11
Step-by-step explanation:
EQ is half of EG
so 22/2 = 11
Simply the following ratio 1000:540:780
How can you use problem-solving strategies in solving personal, professional, and mathematical problems? Explain in 5-7 sentences and I WILL MARK YOU THE BRAINLIEST!!!
Answer:
You are fortunate that there are several excellent algorithms textbooks on the market. Many of them (including Introduction to Algorithms) have material on not just the algorithms, but the techniques you can use to develop algorithms. I recommend that you learn techniques such as divide-and-conquer, dynamic programming, greedy algorithms, and amortized analysis.
Step-by-step explanation:
Hope this answer helps you :)
Have a great day
Mark brainliest
When trying to solve a certain problem, different strategies must be applied that have the ability to solve the question in the most favorable way.
Thus, as a first step, the problem that is taking place, and the severity of it, must be identified. Then, proposals for solving the problem must be prepared, considering the pros and cons of each one, as well as their eventual cost. Subsequently, a main option and a plan B must be chosen with which to solve the question. Finally, the resolution plan must be executed.Learn more in https://brainly.com/question/7208889
Help please!!! I don’t understand this question
Answer:
B) ASA - angle side angle
Hope it help
how do you write .00057 1/2 in words
Answer:
Step-by-step explanation:
visit the following;
https://sciencing.com/write-fractions-words-4443134.html
You used (formula in screenshot) when calculating variance and standard deviation. An alternative formula for the standard deviation that is sometimes convenient for hand calculations is shown below. You can find the sample variance by dividing the sum of squares by n-1, and the sample standard deviation by finding the square root of the sample variance. Complete parts (a) and (b) below.
Answer:
[tex]Varianve = 3.842[/tex]
[tex]SD = 1.960[/tex]
Step-by-step explanation:
Given
See attachment for data
First, calculate [tex]\sum x^2[/tex]
[tex]\sum x^2 = 18^2 + 17^2 +20^2 + 19^2 + 20^2 + 16^2 + 16^2 + 15^2 + 18^2+14^2 +19^2 + 19^2+18^2+17^2 + 16^2+20^2+16^2+18^2+14^2+20^2[/tex]
[tex]\sum x^2 = 6198[/tex]
Calculate [tex]\sum x[/tex]
[tex]\sum x = 18 + 17 +20 + 19 + 20 + 16 + 16 + 15 + 18+14 +19 + 19+18+17 + 16+20+16+18+14+20[/tex]
[tex]\sum x = 350[/tex]
So, we have:
[tex]SS_x = \sum x^2 -\frac{(\sum x)^2}{n}[/tex]
[tex]SS_x = 6198 -\frac{350^2}{20}[/tex]
[tex]SS_x = 6198 -\frac{122500}{20}[/tex]
[tex]SS_x = 6198 -6125[/tex]
[tex]SS_x = 73[/tex]
Solving (a): The variance
[tex]Varianve = \frac{SS_x}{n-1}[/tex]
[tex]Varianve = \frac{73}{20-1}[/tex]
[tex]Varianve = \frac{73}{19}[/tex]
[tex]Varianve = 3.842[/tex]
Solving (b): The standard deviation
[tex]SD = \sqrt{Variance}[/tex]
[tex]SD = \sqrt{3.842}[/tex]
[tex]SD = 1.960[/tex]
please show your work
Surface area of 5 sides of square = 5a²= 5×8.2×8.2=336.2 Cm²
Surface area of pyramid= a²+2a √a²/4+h²= 8.2²+2×8.2√67.24/4+ 4.41= 142.79
Surface area of composite shape = 336.2+142.79-67.24= 411.75~ 411.8 Cm² !
At the playground, the new sandbox was 10 meters wide and had an area of 60 square meters. How long is the sandbox?
Answer:
6 meters
Step-by-step explanation:
Area is length times width. If the width is 10 and the area is 60, then you would find 10 times ??? equals 60. Or 60 divided by 10. which is 6
ally and bo share 60$ in the ratio 1:4 how much money does bo get
Answer: $240
Step-by-step explanation:
So 60 represents the 1, so multiply 60 by 4
Find the circumference of the circle.
Chris was given 1/3 of the 84 cookies in the cookie jar. He ate 3/4 of the cookies that he was given. How many cookies did Chris eat?
Answer:
21 cookies
Step-by-step explanation:
First we know that Chris was given a third of 84 cookies so we can start working on this problem by figuring out what a third of 84 is. We can do this by multiplying 84 by 1/3 or just dividing by 3, which gives us: 84/3 = 28
So now we know that Chris was given 28 cookies, we can figure out what 3/4 of that is to work out how many cookies he ate. 28 x (3/4) = 21 cookies.
Chris ate 21 cookies.
Hope this helped!
Answer:
21 cookies
Step-by-step explanation:
1/3 × 84 = 28
3/4 × 28 = 21
why is the solution to the following equation? x+(-21)=8
Answer:
x = 29
Step-by-step explanation:
[tex]x+(-21)=8[/tex]
[tex]29+(-21)=8[/tex]
[tex]29-21=8[/tex]
[tex]x=29[/tex]