Answer:
x = 28 cm
Step-by-step explanation:
Given:
Area of link shaded regions = 84 cm²
Required:
The value of x (diameter of the semicircle/length of the rectangle)
Solution:
Diameter of the semicircle = 2r = x
Length of rectangle (L) = 2r = x
Radius of semicircle (r) = ½x
Width of rectangle (W) = radius of semicircle = ½x
Use 3.14 as π
Area of the link shaded regions = area of rectangle - area of semicircle
Thus:
Area of the link shaded regions = (L*W) - (½*πr²)
Plug in the values
84 = (x*½x) - (½*3.14*(½x)²)
84 = x²/2 - (1.57*x²/4)
84 = x²(½ - 1.57/4)
84 = x²(0.5 - 0.3925)
84 = x²(0.1075)
Divide both sides by 0.1075
84/0.1075 = x²
781.4 = x²
√781.4 = x
27.9535329 = x
x = 28 cm
Please look at the image
Answer:
[tex]n \leqslant 4[/tex]
Step-by-step explanation:
[tex] - 3n - 5 \geqslant - 17[/tex]
[tex] - 3n \geqslant - 12[/tex]
[tex] \frac{ - 3n}{ - 3} \leqslant \frac{ - 12}{ - 4} [/tex]
[tex]n \leqslant 4[/tex]
Dajuan is painting a mural on a rectangular
wall. The wall is 14.5 feet long and 10 feet
wide. So far, his mural covers 60% of the wall.
Dajuan will paint the remaining part of the wall
over the next four days. He will paint the same
amount of the wall, in square feet, on each of
those four days. How much of the wall, in
square feet, will Dajuan paint on each of the
next four days? Explain how you arrived at
your answer.
Answer:
Every day Dajuan will paint 14.5 square feet of the wall.
Step-by-step explanation:
Since Dajuan is painting a mural on a rectangular wall, which measures 14.5 feet long and 10 feet wide, and so far, his mural covers 60% of the wall, and Dajuan will paint the remaining part of the wall over the next four days, painting the same amount of the wall, in square feet, on each of those four days, to determine how much of the wall, in square feet, will Dajuan paint on each of the next four days, the following calculation must be performed:
((14.5 x 10) x 0.4) / 4 = X
(145 x 0.4) / 4 = X
58/4 = X
14.5 = X
Therefore, every day Dajuan will paint 14.5 square feet of the wall.
Calculate the P-value for the given scenario. Use 4 decimal places.:
Employees at a construction and mining company claim that the mean salary of the company's mechanical engineers is less than that of the one
of its competitors, which is $68,000. A random sample of 20 of the company's mechanical engineers has a mean salary of $66,900. Assume the
population standard deviation is $5500 and the population is normally distributed.
Answer:
The p-value is 0.1867.
Step-by-step explanation:
Employees at a construction and mining company claim that the mean salary of the company's mechanical engineers is less than that of the one of its competitors, which is $68,000.
At the null hypothesis we test that the salary is the same of the competitor, that is:
[tex]H_0: \mu = 68000[/tex]
At the alternate hypothesis, we test that it is more than 68000. So
[tex]H_a: \mu > 68000[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
68000 is tested at the null hypothesis:
This means that [tex]\mu = 68000[/tex]
A random sample of 20 of the company's mechanical engineers has a mean salary of $66,900. Assume the population standard deviation is $5500.
This means that [tex]n = 20, X = 66900, \sigma = 5500[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{66900 - 68000}{\frac{5500}{\sqrt{20}}}[/tex]
[tex]z = -0.89[/tex]
P-value:
The pvalue is the probability of finding a sample mean below 66900, which is the pvalue of z = -0.89.
Looking at the z-table, z = -0.89 has a pvalue of 0.1867.
The p-value is 0.1867.
Jasmine is making 4 types of muffins. Each recipe uses 3/4 cup of sugar.
Answer: The answer is 3
The quantity y varies directly with the square of x. If y=24 when x=3, find y when x is 4
Answer:
[tex]y = \frac{384}{9}[/tex]
Step-by-step explanation:
Given
[tex]y\ \alpha\ x^2[/tex] --- direct variation
[tex](x,y) = (3,24)[/tex]
Required
y when x = 4
[tex]y\ \alpha\ x^2[/tex]
Express as an equation
[tex]y = kx^2[/tex]
Substitute: [tex](x,y) = (3,24)[/tex]
[tex]24 = k*3^2[/tex]
[tex]24 = k*9[/tex]
Solve for k
[tex]k = \frac{24}{9}[/tex]
To solve for y when x = 4, we have:
[tex]y = kx^2[/tex]
[tex]y = \frac{24}{9} * 4^2[/tex]
[tex]y = \frac{24}{9} * 16[/tex]
[tex]y = \frac{24 * 16}{9}[/tex]
[tex]y = \frac{384}{9}[/tex]
given that set C is the negative integers greater than -7, which element of set C are less than or qual to -3? (enter your answer as a comma-separated list
9514 1404 393
Answer:
-6, -5, -4, -3
Step-by-step explanation:
Integers greater than -7 include ... -6, -5, -4, ....
Integers less than or equal to -3 include ... -3, -4, -5, ....
The set of integers in the range -7 < n ≤ -3 is ...
{-6, -5, -4, -3}
there is a picture. please help!!!!
Answer:
the answer should be B becaise just multiply and then round up that is what I got good luck
Rewrite all three fractions with the lowest common denominator.
Answer:
[tex] - \frac{2}{4 } = - \frac{16}{32} [/tex]
[tex] - \frac{6}{8} = - \frac{24}{32} [/tex]
[tex] - \frac{13}{32} = [/tex]
remains the same
I will give you Brainiest if you are right.
Answer:
Students 1 & 4
Step-by-step explanation:
An expression has NO equal sign, EQUATIONS have equals.
2 & 3 have equals which makes then equations.
~R3V0
One can of Mountain Dew costs $1.25 in a vending machine.
A 12-pack of Mountain Dew costs $3.49 at the grocery store.
How much money would you save by purchasing a dozen cans of Mountain Dew at the grocery store instead of a dozen at the vending machine?
$2.24
$0.96
$11.51
$12.49
Find the volume of the cone
12 cm
5 cm
V = [?] cm
Round to the nearest tenth.
Enter
Answer:
314.2 cm³
Step-by-step explanation:
Volume of a cone [tex] = \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]
The volume of the cone
[tex] = \frac{1}{3} \times \pi \times {5}^{2} \times 12[/tex]
[tex]= 314.15926...[/tex]
= 314.2 cm³ (rounded to the nearest tenth)
Answer: 314
Step-by-step explanation:
porque es matematicas nos piden buscar la x?
Answer:
Em matemática, costumamos usar a letra “x” para representar a quantidade desconhecida. Mas agora x está em toda parte em nossa sociedade. As pessoas usam “x” para representar algo inexplicável ou desconhecido, como raio-X, arquivo X e i hope that helps :)
CAN SOMEONE HELP ME WITH THIS 25 POINTS TY :)
Answer:
Hello!
Here are the coordinates and a picture example!
Original coordinates: -3, -5
New coordinates: 3, -5
Hope that helps!
apply the Pythagorean theorem to find the distance between two points (to the nearest tenth). which statements are correct
Answer:
options pls. or any image.......................................
The distance between two points is √29 unit.
What is Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, also known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
We have the points (-2, 3) and (3, 1).
Using Distance formula
= √(1-3)² + (3 - (-2))²
= √ (-2)² + (5)²
= √ 4 + 25
= √29 unit
Thus, the distance between two points is √29 unit.
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11. Explain how to evaluate the expression 9 +(45 x 2) = 10.
The Answer Is 18
Order Of Operation laws says that you must do the parentheses first, 45x2.
45x2=90
The next thing you must do is divide 90 by 10 since division is before addition.
90/10=9
Now combine like terms.
9+9=18
PLEASE HELP SO I CAN GO EAT LUNCH!!
Answer:
Average low temp. = 6. The fourth number is 9.
Step-by-step explanation:
To find the average of 7 low temperatures, add them and divide the sum by 7.
Average low temp. = (5 + 8 + 6 + 5 + 10 + 7 + 1) / 7 = 42 / 7 = 6
The mean is the average. Call the missing number x.
There are four numbers, three of which are given. Add all the number, including the unknown x, then divide the sum by 4. The result is 7 (given in the problem).
[tex]\frac{5+7+7+x}{4}=7\\\frac{19+x}{4}=7\\19+x=28\\x=9[/tex]
Help pls show work if needed
Answer: The mode is 12
Step-by-step explanation: It is the most common number in the data set.
If you add Natalie’s age and Fred’s age, the result is 41. If you add Fred’s age to 3 times Natalie’s age, the result is 67. Find how old Fred and Natalie are.
Answer:
Natalie is 13 years old, while Fred is 28 years old.
Step-by-step explanation:
Given that if you add Natalie’s age and Fred’s age, the result is 41, and if you add Fred’s age to 3 times Natalie’s age, the result is 67, to find how old Fred and Natalie are, the following calculation must be performed:
N + F = 41
3N + F = 67
(67 - 41) / 2 = N
26/2 = N
13 = N
13 x 3 + F = 67
39 + F = 67
F = 67 - 39
F = 28
28 + 13 = 41
Therefore, Natalie is 13 years old, while Fred is 28 years old.
A bakery offers a sale price of $2.80 for 3 muffins. What is the price per dozen?
Answer: 11.2$
Step-by-step explanation:
Need help please right answers
Answer:
B
Step-by-step explanation:
y-intercept is where x is zero, so we must look at where the y-iterceot is crossed
(NO LINKS)
How much compound interest is earned on a deposit of $6000 at 2.25%, compounded daily for 22 days?
Answer:
Total: $9,789.13
Interest: $3,789.13
Step-by-step explanation:
A local boys club sold 136 bags of mulch and made a total of $538. It sold two types of mulch: hardwood for $4.25 a bag and pine bark for $3.75 a bag. How many bags of each kind of mulch did it sell?
Answer:
56 hardwood 80 pine bark
Step-by-step explanation:
H = hardwood B= pine bark
B +H = 136
B = (136-H)
4.25 H + 3.75 (136-H) = 538
4.25H + 510 - 3.75H = 538
0.5 H = 28
1H = 56 (56 Hardwood)
136-56= 80
56x 4.25 + 80 x 3.75 = 538
$238 + $300 = $538
Which ordered pair is in the solution set of 0.5x - 2y ≥ 3?
Answer:
C
Step-by-step explanation:
The answer is c because when 2, -1 is plugged into the equation, you get
.5(2) - 2(-1) >/= 3
when solved -
1 + 2 >/= 3 -
3 >/= 3
and this is in the solution set because three is equal than or greater to three
please answer this for me
Answer:
A
Step-by-step explanation:
Helloooo help me out thanks youuuuuu
Answer:
C. 162.5 sq ft.
Step-by-step explanation:
Given the following data;
S.A of smaller cylinder, S1 = 65 ft²
Ratio = 2:5 = 2 + 5 = 7
Let the total surface area be x.
S1 = 2/7 * x = 65
S1 = 2x = 65 * 7
S1 = 2x = 455
x = 455/2
x = 227.5 ft²
To find the surface area of the larger cylinder;
S2 = 5/7 * 227.5
S2 = 1137.5/7
S2 = 162.5 ft²
A box has a length of 15 centimeters, a width of 22 centimeters, and a height of 9 centimeters. What is the surface area of the box? 1,326 cm 2 92 cm 2 5,940 cm 2 663 cm 2
The surface area of the figure will be equal to 1326 square meters.
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called as the surface area.
Given that:-
A box has a length of 15 centimetres, a width of 22 centimetres, and a height of 9 centimetres.The surface area will be calculated as:
SA = 2 { LW + LH + WH )
SA = 2 { ( 9 x 12) + (15 x 22 ) + (15 x 9 )}
SA = 1326 square meters.
Therefore the surface area of the figure will be equal to 1326 square meters.
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which deduction is optional?
a.federal income tax
b. life insurance
c.medicare
d.social security
Answer:
Life insurance
Step-by-step explanation:
The rest are governm taxes
paulina made green paint by mixing blue paint and yellow paint in the ratio 3 : 4. she used 600 milliliters of yellow paint. find the volume of green paint paulina made
Which statement correctly compares the two functions on the interval [-1,2]?
Answer:
Option A.
Step-by-step explanation:
Function f:
For x between -1 and 2, the values of f(x) increase, which means that f(x) is increasing.
Function g:
[tex]g(x) = -18(\frac{1}{3})^x + 2[/tex]
Between -1 and 2:
[tex]g(-1) = -18(\frac{1}{3})^{-1} + 2 = -18*3 + 2 = -54 + 2 = -52[/tex]
[tex]g(0) = -18(\frac{1}{3})^{0} + 2 = -18*1 + 2 = -18 + 2 = -16[/tex]
[tex]g(1) = -18(\frac{1}{3})^{1} + 2 = -18*\frac{1}{3} + 2 = -6 + 2 = -4[/tex]
[tex]g(2) = -18(\frac{1}{3})^{2} + 2 = -18*\frac{1}{9} + 2 = -2 + 2 = 0[/tex]
Both are increasing.
However, g starts with a lower value, and finishes with a higher value, which means that function g increases at a faster average rate, and the correct answer is given by option A.
The following is a random sample of the annual salaries of high school counselors in the United States. Assuming that the distribution of salaries is approximately normal, construct a 98% confidence interval for the mean salary of high school counselors across the United States. Round to the nearest dollar. $45,860,$38,860,$64,820,$63,480,$36,710,$50,410,$33,080
Solution :
x [tex]$(x-\overline x)$[/tex] [tex]$(x-\overline x)^2$[/tex]
45860 -1742.8571 3037551.0204
38860 -8742.8571 76437551.0204
64820 17217.1429 296430008.1633
63480 15877.1429 252083665.3061
36710 -10892.8571 118654336.7347
50410 2807.1429 7880051.0204
33080 -14522.8571 210913379.5918
333220 0.0000 965436542.8571
Sample size, n = 7
Mean = [tex]$\frac{\sum x}{n}=\frac{333220}{7}$[/tex]
= 47602.8571
Variance = [tex]$\frac{(\sum (x- \overline x))^2}{(n-1)}=\frac{965436542.8571}{7-1}$[/tex]
= 160906090
Standard deviation = [tex]$\sqrt{Variance} = \sqrt{160906090}$[/tex]
= 12684.876
a). df = n - 1
= 7 - 1
= 6
Level of significance, α = 0.02
Critical, [tex]$t_c = 3.143$[/tex]
b). Sample mean, [tex]$\overline x = 47602.8571$[/tex]
Sample standard deviation, s = 12684.876
Sample size, n = 7
c). 98% confidence interval = [tex]$\overline x \pm t_c \times \frac{s}{\sqrt n}$[/tex]
[tex]$=47602.8571 \pm 3.143 \times \frac{12684.876}{\sqrt 7}$[/tex]
[tex]$=(32533.96,62671.76)$[/tex]