A rectangular chair cushion
measures 4 inches long, 12 inches
wide, and 3 inches high. How many square inches of fabric would you need to cover the cushion
Answer:
144 square inches.
Step-by-step explanation:
4*12*3=144
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 404 gram setting. It is believed that the machine is underfilling the bags. A 27 bag sample had a mean of 402 grams with a variance of 676. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?
Answer:
There is no sufficient evidence to support the claim that the bags are underfilled
Step-by-step explanation:
We are given;
n = 27 bags
Sample mean;X = 402 gram
Population mean;μ = 404 gram
Variance = 676
We know that, standard deviation(σ) = √variance
Thus;
σ = √676
σ = 26
The hypotheses are;
Null hypothesis; H0: μ = 404
Alternative hypothesis; HA: μ < 404
Let's find the z-score from the formula;
z = (X - μ)/(√σ/n)
z = (402 - 404)/√(26/27)
z = -2.04
From the z-distribution table attached, we have a p-value of 0.02068
This is less than the significance value of 0.01 and thus we will reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that the bags are underfilled
Janice correctly answered 21 of the 24 question. What percent of the questions did she answer correctly?
Math-Limits and Derivative. Could anybody help me,please ?
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]\displaystyle f'(0)=\lim_{x\rightarrow0} {\dfrac{f(x)-f(0)}{x-0}}\\\\=\lim_{x\rightarrow0} {\dfrac{\dfrac{\sqrt{1+x}-1}{x}-k}{x}}\\\\=\lim_{x\rightarrow0} {\dfrac{\dfrac{\sqrt{1+x}-1-kx}{x}}{x}}\\\\=\lim_{x\rightarrow0} {\dfrac{\sqrt{1+x}-1-kx}{x^2}}\\[/tex]
Thank you
The yearly attendance at a local movie theater is 82,000 and grows continuously at a rate of 5.1% each year. What is the approximate attendance at the movie theater in ten years? (3 points) a 136,554 b 85,552 c 134,847 d 123,820
Answer:
c. 134,847
Step-by-step explanation:
82,000 x (1.051)^10 = 82,000 x 1.64447456 = 134,847
what is formula for circumfrences
The circumference of a circle, which is another way of saying the perimeter of a circle, can be found using the formula 2πr.
Note that π represents the irrational number 3.14159... which
rounds to 3.14 and r represents the radius of the circle.
Therefore, since π = 3.14, another way of writing the formula
for the circumference of a circle is 2 · 3.14r or 6.28r.
Answer:
circumference = 2 π r
or
circumference = π d
Step-by-step explanation:
r = radius of a circle
d = diameter
therefore
circumference = 2 π r
or
circumference = π d
The dependent variable y is missing in the given differential equation. Proceed as in Example 1 and solve the equation by using the substitution u = y'.
y'' + (y' )^2 + 4 = 0
Answer:
y = In | cos(2x + c ) | + c
Step-by-step explanation:
y" + (y')^2 + 4 = 0
substituting u = y'
u' + u^2 + 4 = 0
hence : u' = - (u^2 + 4 )
[tex]\frac{u'}{-(u^2 + 4)}[/tex] = 1 ------- (1)
integrating both sides of the equation 1
[tex]1/2 \int\limits^1_1 {\frac{2du}{(u^2+4)} } \, = x + c[/tex]
x + c = [tex]- \frac{1}{2} arc tan (\frac{u}{2} )[/tex] hence u = -2 tan(2x + c )
remember u = y'
y' = -2 tan(2x + c) ------ (2)
integrating both sides of the equation 2
y = ∫ [tex]\frac{-sin u}{cos u } du[/tex]
therefore Y = In | cosu | + c
y = In | cos(2x + c ) | + c
Round 141.999 to the next tenth
Answer:
142
Step-by-step explanation
How did the first line get to the second line??? (Check Picture)
Step-by-step explanation:
[tex]15( \frac{11\pi}{6} ) \\ 15 \div 3 = 5 \\ 6 \div 3 = 2 \\ = 5( \frac{11\pi}{2} )[/tex]
[tex]11 \times 5 \\ = \frac{55\pi}{2} [/tex]
Simplify to create an equivalent expression 11/12-1/6q+5/6q-1/3
Answer: 7/12 + 2/3q
Step-by-step explanation:
[tex]\frac{11}{12} - \frac{1}{6}q + \frac{5}{6}q - \frac{1}{3}[/tex] Combine like terms subtract 1/3 from 11/12 and add -1/6q and 5/6q.
[tex]\frac{11}{12} - \frac{1}{3} = \frac{7}{12}[/tex]
[tex]-\frac{1}{6}q + \frac{5}{6} q = \frac{4}{6}[/tex]q = 2/3 q
Solve −2x − 15 = 6x + 9. (1 point) 3 −3 −1 6
Answer:
-2x-15=6x+9
-2x-6x=9+15
-8x=24
x=-24/8
x=-3
PLEASE HELP !!! The height of a rectangle is twice the width and the area is 32. Find the dimensions.
Answer:
The rectangle has a width of 4 and a height of 8
Step-by-step explanation:
Let the height of the rectangle be H and the width be W.
We know the height of the rectangle is twice the width, so:
H = 2W
The area of a rectangle, A, is given by A = W * H, so in this case:
32 = W * 2W
32 = 2W²
W² = 16
W = 4
Knowing that the width is 4, the height must be 8. This gives us an area of 32.
Which statement is true?
A. This scatter plot has no clusters and no outliers.
B. This scatter plot has one cluster and no outliers.
C. This scatter plot has one cluster and three outliers.
D. This scatter plot has one cluster and one outlier.
A cluster is a small group of dots close together. An outlier is a single dot far away from the rest of the dots.
The above graph has a small cluster around y 6&7 and has an outlier at (9,5)
The answer should be D.
Answer:
The correct answer is D. This scatter plot has one cluster and one outlier.
Step-by-step explanation:
From looking at the scatterplot, the majority of the points are collected on the upper left side of the coordinate grid, creating a cluster. This just means that these data points are located close to one another.
If we continue to look at the scatterplot, we can see that there is one data point at approximately (9, 5.25) that is very far from the other data points. This point is considered to be an outlier because it does not follow the general trend of the other data points and changes the data analysis significantly if included in the calculations.
Hope this helped!
Businesses in a country are listed by size: small, medium, and large. Explain why business size is an example of an ordinal-scaled variable. A. The size of a business is ordinal-scaled because it has numerical values that arise from a measuring process. B. The size of a business is ordinal-scaled because it has values that represent quantities. C. The size of a business is ordinal-scaled because it has values that can be used as an order or rank of a categorical variable. D. The size of a business is ordinal-scaled because it has numerical values that arise from a counting process.
Answer: C. The size of a business is ordinal-scaled because it has values that can be used as an order or rank of a categorical variable.
Step-by-step explanation: Ordinal variables are simply categorical in nature just like nominal variables, however, the difference exists in the fact that ordinal labels posses an ordered rank or level unlike nominal variables. Though the extent or width of the difference between these labels cannot be ascertained. In the scenario above, size of businesses are labeled qualitatively with labels such as : small, medium and large. This labels depicts and follow a certain order with small being the least, then medium, then large. Telling us large businesses are superior in size to small and medium and medium is superior to large. Though the extent of the difference cannot be accurately ascertained.
(-2÷3)^-3 ÷ x = (9÷8)^-2
Answer:
- 3⁷/2⁹
Step-by-step explanation:
(-2÷3)⁻³ ÷ x = (9÷8)⁻²-(2⁻³)×3⁽⁻¹⁾ˣ⁽⁻³⁾ ÷ x = (3²)⁻²×(2⁻³)⁻²-2⁻³×3³÷x = 3⁻⁴×2⁶x = -2⁻³×3³ ÷ (3⁻⁴×2⁶)x = - 2⁻³⁻⁶×3³⁻⁽⁻⁴⁾x = -2⁻⁹×3⁷x = - 3⁷/2⁹Suppose Kaitlin places $ 4000 in an account that pays 18% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
sa
(b) Find the amount in the account at the end of 2 years.
Answer:
a) $4720
b) $5569.60
Step-by-step explanation:
Initial amount = $4000
Interest rate = 18% PA compounded
Amount after 1 year
$4000*1.18 = $4720Amount after 2 years
$4720*1.18 = $5569.60Solve each absolute value equation and match them with the correct solution.
Answer:
Step-by-step explanation:
First we must understand that absolute value of a function returns both positive and negative function.
1) Given |x-6| = 5
For the positive value of the function:
x-6 = 5
Add 6 to both sides
x-6+6 = 5+6
x = 11
For the negative function:
-(x-6) = 5
Open the parentheses
-x+6 = 5
Subtract 6 from both sides
-x+6-6 = 5-6
-x = -1
x = 1
Hence x = 1, x = 11
2 ) Given |3x-7| = 12
For the positive value of the function:
3x-7 = 12
Add 7 to both sides
3x-7+7 = 12+7
3x = 19
x = 19/3
For the negative function:
-(3x-7) = 12
Open the parentheses
-3x+7 = 12
Subtract 7 from both sides
-3x+7-7 = 12-7
-3x = 5
x = -5/3
Hence x = 19/3, x = -5/3
3) Given |2x+9| - 10= 5
For the positive value of the function:
2x+9-10= 5
2x-1 = 5
Add 1 to both sides
2x-1+1 = 5+1
2x = 6
x= 3
For the negative function:
-(2x+9)-10 = 5
Open the parentheses
-2x-9-10 = 5
-2x-19 = 5
Add 19 to both sides
-2x-19+19 = 5+19
-2x= 24
x = -24/2
x= -12
Hence x = 3, x = -12
4) ) Given |5x-3|+12 = 4
For the positive value of the function:
5x-3+12= 4
5x+9 = 4
Subtract 9 from both sides
5x+9-9 = 4-9
5x = -5
x= -1
For the negative function:
-(5x-3)+12= 4
Open the parentheses
-5x+3+12 =4
-5x+15 = 4
Subtract 15 from both sides
-5x+15-15 = 4-15
-5x = -11
x = 11/5
Hence x = -1, x = 11/5
trig: Solve Quadratic Equations by Factoring help with 2b and 2c
Answer:
2b)x=1/3 or x= -4
2c) x= 0 or x= -2/3
Step-by-step explanation:
To factor ax² + bx + c, use the AC method.
Multiply a and cFind factors of ac that add up to bDivide those two factors by a. Reduce the fractions.The numerators are the constants, and the denominators are the coefficients.(b) 3x² + 11x − 4 = 0
a = 3, b = 11, c = -4ac = (3)(-4) = -12Factors of -12 that add up to 11 are 12 and -1.Divide by 3: -1/3 and 12/3 = 4/1The factors are 3x − 1 and x + 4.(3x − 1) (x + 4) = 0
3x − 1 = 0, or x + 4 = 0
x = 1/3, or x = -4
(c) 12x² + 8x = 0
Here, you can simply factor the greatest common factor, 4x.
4x (3x + 2) = 0
4x = 0, or 3x + 2 = 0
x = 0, or x = -2/3
What is the length of CD to the nearest 10th?
Answer:
[tex]\huge \boxed{\mathrm{10.3 \ units}}[/tex]
Step-by-step explanation:
To solve for CD, we can create a right triangle.
Where CD becomes the hypotenuse.
The length of the base of the triangle is 9 units.
The length of the height of the triangle is 5 units.
Apply Pythagorean theorem to solve for the hypotenuse.
[tex]\sf hypotenuse = \sqrt{(base )^2 +(height )^2 }[/tex]
[tex]c=\sqrt{9^2 +5^2 }[/tex]
[tex]c=\sqrt{106}[/tex]
[tex]c \approx 10.29[/tex]
what is the range of the function f(x)=(x+4)²+5
Answer:
[tex]Range=\left \{y|y\geq 5\right \}[/tex]
Step-by-step explanation:
Since given the expression, this represents graphically a parabola with arms pointing up, and a vertical translation of its vertex 5 units up, then the range of the function must be all the y values such that they are greater or equal to 5. This is written as:
[tex]Range=\left \{y|y\geq 5\right \}[/tex]
Find the solution of the system of equations
shown on the graph.
Answer:
(-4, 3)
Step-by-step explanation:
From the graph, it looks like the two lines intersect at pint (-4, 3).
i will give you brainliest if you right down the answer and explain it
Answer:
[tex]\sqrt{113\\[/tex]
Step-by-step explanation:
set the problem up like this:
[tex]\sqrt{(x2-x1)^{2} +(y2-y1)^2[/tex]
(x1,y1) (x2,y2)
x1=-3
y1+3
x2=5
y2=-4
The equation should look like this:
[tex]\sqrt{(5-(-3))^2 + (-4-3)^2[/tex]
Then you solve it and 113 is the square root in between.
Hope it helps...
Liar has a red ribbon that is 2 and 1/12 incest long. She has a blue ribbon that is 4 times as many investors long how many investors long is the blue ribbon
Answer:
I think it would be 8 and 1/3 inches long
Step-by-step explanation:
P.S. You spelled inches wrong
how do i solve this absolute value equation |3x-2|+4=7?
Answer:
{3x-2}+4=10
Step-by-step explanation:
A candy factory wants to compare a new machine to their current machine. Both machines produce y boxes of candy for every hour x. The current machine is represented by the equation f(x). The new machine is represented by the equation g(x). f(x) = 15x + 90 g(x) = 30x + 30 After what number of hours will the amount of candy produced be the same for both machines?
Answer:
In 4 hours.
Step-by-step explanation:
Just equate f(x) = g(x). So:
15x + 90 = 30x + 30
60 = 15x
x = 4 hours.
In 4 hours the amount of candy produced be the same for both machines.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
It is given that A candy factory wants to compare a new machine to their current machine. Both machines produce y boxes of candy for every hour x. The current machine is represented by the equation f(x). The new machine is represented by the equation g(x). f(x) = 15x + 90 g(x) = 30x + 30.
The value of time will be calculated below:-
Just equate f(x) = g(x).
15x + 90 = 30x + 30
60 = 15x
x = 4 hours.
Therefore, In 4 hours the amount of candy produced is the same for both machines.
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the remains of an ancient ball court include a rectangular playing alley with a perimeter of about 64 M. the length of the alley is 2 times the width. find the length and the width of the playing alley
Answer:
[tex]Length = \frac{64}{3}m[/tex]
[tex]Width= \frac{32}{3}m[/tex]
Step-by-step explanation:
Given
[tex]Perimeter = 64m[/tex]
[tex]Length = 2 * Width[/tex]
Required
Determine the length and the width
Since the alley is rectangular, the perimeter is as follows;
[tex]Perimeter = 2 (Length * Width)[/tex]
Substitute 64m for Perimeter
[tex]64m = 2(Length + Width)[/tex]
Substitute 2 * Width for Length
[tex]64m = 2(Width+ 2 * Width)[/tex]
[tex]64m = 2(Width+ 2 Width)[/tex]
[tex]64m = 2(3 Width)[/tex]
[tex]64m = 6Width[/tex]
Divide both sides by 6
[tex]Width= \frac{64m}{6}[/tex]
[tex]Width= \frac{32}{3}m[/tex]
Recall that
[tex]Length = 2 * Width[/tex]
[tex]Length = 2 * \frac{32}{3}m[/tex]
[tex]Length = \frac{64}{3}m[/tex]
2. Solve for z and express your answer in interval notation: 10 – 4z < 20
Answer:
z > -5/2
Step-by-step explanation:
Since both sides are divided by a negative number, the equality is switched.
10 - 4z < 20
(10 - 4z) - 10 < 20 - 10
-4z < 10
(-4z)/-4 < 10/-4
z > -5/2
The solution for z will be;
⇒ z ∈ (- 2.5 , ∞ )
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ 10 - 4z < 20
Now,
Since, The inequality is,
⇒ 10 - 4z < 20
Solve for z as;
⇒ 10 - 4z < 20
⇒ 10 - 4z + 4z < 20 + 4z
⇒ 10 < 20 + 4z
⇒ 10 - 20 < 4z
⇒ - 10 < 4z
⇒ - 2.5 < z
⇒ z ∈ (- 2.5 , ∞ )
Thus, The interval notation is,
⇒ z ∈ (- 2.5 , ∞ )
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A random sample of 1700 workers in a particular city found 578 workers who had full health insurance coverage. Find a 95% confidence interval for the true percent of workers in this city who have full health insurance coverage.
Answer: (31.75%, 36.25%)
Step-by-step explanation:
Let p be the proportion of workers in this city who have full health insurance coverage.
As per given,
Sample size : n= 170
Number of workers who had full health insurance coverage.=578
i.e. sample proportion: [tex]\hat{p}=\dfrac{578}{1700}\approx0.34[/tex]
Also, z-score for 95% confidence level : 1.96
Formula to find the confidence interval for p :
[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]0.34\pm (1.96)\sqrt{\dfrac{0.34(1-0.34)}{1700}}[/tex]
[tex]=0.34\pm (1.96)\sqrt{0.000132}\\\\=0.34\pm (1.96)(0.011489125)\\\\\approx 0.34\pm0.0225\\\\=(0.34-0.0225,\ 0.34+0.0225)\\\\=(0.3175,\ 0.3625) =(31.75\%,\ 36.25\%)[/tex]
Hence, a 95% confidence interval for the true percent of workers in this city who have full health insurance coverage= (31.75%, 36.25%)
Help meeeee time card. Weekly time card $11hr
Answer: it would be $96.25
Step-by-step explanation:
In the am, it’s 4 hours. 4x11= $44
In the pm it’s 4 hours and 45mins. 4x11=44
The for the 45 mins. Multiply 45x11= 495 then divide by 60. That gives you $8.25. When you add them all together, you get 96.25
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!
Answer:
Twelve tickets cost $30 --> True
Thirty tickets cost $12 --> False
Each additional costs $2.50 --> True
The table is a partial rep --> True
ordered pairs --> False
Step-by-step explanation:
Twelve tickets cost $30 --> True, you can literally see that in the table
Thirty tickets cost $12 --> False, 30 is not in the table so you don't have that information. Besides, $12 is an unlikely low value for so many tickets.
Each additional costs $2.50 --> True, you can see the difference in the TotalCost column to be consistently 2.50.
The table is a partial rep --> True, values below 11 are not shown for example.
ordered pairs --> False --> Then the x value should be first, e.g., (11, 27.50), since the cost y is a function of the number x.