Answer:
4.9 units
Step-by-step explanation:
The area of a circle is πr².
πr² = 24π
Cancel π on both sides.
r² = 24
Take the square root on both sides.
r = √24
r ≈ 4.898979
The radius is 4.9 units.
Answer: The radius is 4.9
520 after a 30% increase
Answer:
676
Step-by-step explanation:
Convert the percentage to a decimal.
30% = 0.3
Multiply the number by the decimal.
520 × 0.3 = 156
Add this number by the number given.
520 + 156 = 676
whats the square root of 83
Answer:
9.110434
Step-by-step explanation:
√83 ≈ 9.110434
What is 4 2/3 ÷ 1 1/5
Answer:
3 8/9
Step-by-step explanation:
1.) Convert each fraction from a mixed number to a improper fraction (to do that multiply the denominator with the whole number then add the numerator, the improper fraction denominator will remain the same as the mixed number denominator):
14/3 ÷ 6/5
2.) Solve
a. To divide the fractions, Flip the reciprocal, and multiply the fractions
14/3 x 5/6
b. Check if you can reduce the numbers, which you can 14 and 6 can be both divided by 2:
7/3x5/3
c. Multiply fractions (simply by multiplying across):
35/9
3.) Simplify numbers into mixed fraction (or decimal):
3 8/9
Robert uses a wheelbarrow to haul wood from the back yard to his neighbor's house located 9 meters away. If he takes two breaks evenly when pushing the wheelbarrow to its destination, at which distance will he reach his first break?
Robert has 36 pieces to take, but can only take 9 each time. What distance in meters will he travel to move all the wood?
Answer:
3 meters
63 meters
Step-by-step explanation:
In order for his two breaks to occur after even distances, simply divide his total path in three:
[tex]B = \frac{9}{3}\\ B=3\ meters[/tex]
He will reach his first break after 3 meters.
If he can only take 9 pieces at a time the number of trips required is:
[tex]n=\frac{36}{9}\\ n=4[/tex]
Note that he will have to back to the back yard for the first three trips (traveling back the 9 meters path). The total distance traveled is:
[tex]d= 3*(9+9)+9\\d=63\ meters[/tex]
He will travel 63 meters.
I paid twice as much by not waiting for a sale and not ordering on line. Which ofthe following statements is also true?
(a) I paid 200% more than I could have online and on sale.
(b) I paid 100% of what I could have online and on sale.
(c) I paid 200% of what I could have online and on sale.
(d) I paid 3 times what I could have online and on sale.
Answer:
(c) I paid 200% of what I could have online and on sale.
Step-by-step explanation:
The multiplier for a increase of a% is 1 + a/100.
In this question:
You paid twice, which means that the multiplier is 2. So
a is the increase, as a percent.
[tex]1 + \frac{a}{100} = 2[/tex]
[tex]\frac{a}{100} = 1[/tex]
[tex]a = 100[/tex]
You had an increase of 100% on the price. Since the original amount was 100% you paid 100 + 100 = 200%(100% more, 2 times) of what you could have paid.
So the correct answer is:
(c) I paid 200% of what I could have online and on sale.
What is the answer? X=
Answer:
5
Step-by-step explanation:
[tex] \because \triangle ACB \cong \triangle DCE... (given) \\
\therefore \angle A \cong \angle D... (c.a.c.t)\\
\therefore m\angle A = m\angle D\\
\therefore 50\degree = 10x\\\\
\therefore x = \frac{50\degree}{10}\\\\
\huge \orange {\boxed {\therefore x = 5\degree}} [/tex]
Micah mixed 5 ounces of yellow paint with 11 ounces of blue paint. What is the ratio of blue paint to the total amount of paint that Micah used? Write the ratio using a colon and no spaces.
Answer: 11:16
Step-by-step explanation: 11 ounces of blue paint: the total number ounces of paint (adding blue and yellow)
Answer:
5:16
Step-by-step explanation:
The amount of blue paint is 5 oz
The total amount of paint is 16 oz
Make these numbers a ratio of blue to total
Solve for the variables: 3x-4y=17 x-4y=3
Answer:
[tex]3x - 4y = 17ndx - y = 3 \\ 3x - x - 4y + 44y = 17 - 3 \\ 3x - x = 17 - 3 \\ 2x = 17 - 3 \\ 2x = 14 \\ x = 7 \\ \\ 7 - 4y = 3 \\ - 4y = - 4 \\ y = 1[/tex]
Answer:
x = 7
y = 1
Step-by-step explanation:
3x - 4y = 17
x - 4y = 3
Solve x in the second equation.
x = 3 + 4y
Put x as 3 + 4y in the first equation and solve for y.
3(3 + 4y) - 4y = 17
9 + 12y - 4y = 17
9 + 8y = 17
8y = 17 - 9
8y = 8
y = 8/8
y = 1
Put y as 1 in the second equation and solve for x.
x = 3 + 4(1)
x = 3 + 4
x = 7
The CEO of a large manufacturing company is curious if there is a difference in productivity level of her warehouse employees based on the region of the country the warehouse is located. She randomly selects 35 employees who work in warehouses on the East Coast (Group 1) and 35 employees who work in warehouses in the Midwest (Group 2) and records the number of parts shipped out from each for a week. She finds that East Coast group ships an average of 1299 parts and knows the population standard deviation to be 350. The Midwest group ships an average of 1456 parts and knows the population standard deviation to be 297.Using a 0.01 level of significance, test if there is a difference in productivity level. What is the p-value? (Round to four decimal places) p-value =
Answer:
The results of the hypothesis test suggests that there is no difference in productivity level of two warehouses (East Coast and the Midwest Coast).
p-value = 0.0473
Step-by-step explanation:
To perform this test we first define the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, we want to test if there is a difference in productivity level of the two warehouses (East Coast and the Midwest Coast).
Hence, the null hypothesis would be that there isn't significant evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast). That is, there is no difference in the productivity level of two warehouses (East Coast and the Midwest Coast).
The alternative hypothesis is that there is significant evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast).
Mathematically, if the average productivity level of the East Coast group is μ₁, the average productivity level of the Midwest group is μ₂ and the difference in productivity level is μ = μ₂ - μ₁
The null hypothesis is represented as
H₀: μ = 0 or μ₂ = μ₁
The alternative hypothesis is represented as
Hₐ: μ ≠ 0 or μ₂ ≠ μ₁
So, to perform this test, we need to compute the test statistic
Test statistic for 2 sample mean data is given as
Test statistic = (μ₂ - μ₁)/σ
σ = √[(s₂²/n₂) + (s₁²/n₁)]
μ₁ = average productivity level of the East Coast group = 1299 parts shipped
n₁ = sample size of East Coast group surveyed = 35
s₁ = standard deviation of the East Coast group sampled = 350
μ₂ = average productivity level of the Midwest group = 1456 parts shipped
n₂ = sample size of Midwest group surveyed = 35
s₂ = standard deviation of the Midwest group sampled = 297
σ = √[(297²/35) + (350²/35)] = 77.5903160379 = 77.59
We will use the t-distribution as no information on population standard deviation is provided
t = (1456 - 1299) ÷ 77.59
= 2.02
checking the tables for the p-value of this t-statistic
Degree of freedom = df = n₁ + n₂ - 2 = 35 + 35 - 2 = 68
Significance level = 0.01
The hypothesis test uses a two-tailed condition because we're testing in both directions.
p-value (for t = 2.02, at 0.01 significance level, df = 68, with a two tailed condition) = 0.047326
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.01
p-value = 0.047326
0.047326 > 0.01
Hence,
p-value > significance level
This means that we fail to reject the null hypothesis & say that there isn't enough evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast).
Hope this Helps!!!
Are 2b+ b and 3b equivalent expressions?
Answer:
yes
Step-by-step explanation:
2b+b=3b because2+1 = 3
Answer:
the answer is yes
Step-by-step explanation:
yes it is equivalent expression because 2b+b and 3b have the same value and length or numerator which equals yes.
Solve the following system of equations: x − 2y = 14 x + 3y = 9 (1, 12) (−1, −12) (12, −1) (12, 1)
Answer:
work is shown and pictured
answer is c
Answer:
the correct answer among the choices is C
Step-by-step explanation:
If (x^2 – 4) = (x + 2) = x - 2, which polynomial should fill in the blank below?
Hey there! :)
Answer:
2nd choice. (x - 2)
Step-by-step explanation:
Given in the question:
(x²-4) ÷ (x + 2) = x-2
This is an example of difference of squares.
We can rearrange the equation by multiplying both sides by (x+2) to become:
(x² - 4) = x - 2 (x + 2)
Therefore, the binomial that must be multiplied by (x+2) is the second choice, x-2.
Answer: B
Step-by-step explanation:
Help me Please, i will give you branliest
Answer:
35/42 = b/7 and b= 35/6
Step-by-step explanation:
Our base is unkhown so it will be the variable in our equation :
Let A be the area , h the height and b the base A = b*h 35/42 = b/7 this is the equation , let's solve it (35*7)/42 = b (35*7)/ 7*6 =b 35/6 = bso b is 35/6 cm
Work out percentage change to 2 decimal places when price of 97 is decreased to 90
Answer:
7.22?
Step-by-step explanation:
Write a number with 2 decimal places, that is bigger than 4 and 1/5 but smaller than 4.25?
Answer: 4 wholes and 1/5 is 4.20 and you need something greater than that but less than 4.25 which still has only 2 decimals.
What is the equation of a line whose slope is 2 and passes through the point (-6,9)
Answer:
y = 2x + 21
Step-by-step explanation:
Step 1: Write out known variables
y = mx + b
m = 2
y = 2x + b
Step 2: Find b
9 = 2(-6) + b
9 = -12 + b
b = 21
Step 3: Rewrite linear equation
y = 2x + 21
Translate into an algebraic expressions: b is decreased by 40% and decreased again by 40% . What is the result ?
Answer:
Result = 9b/25 or 36b/100
Step-by-step explanation:
The number is b
step 1
b is decreased by 40%
value of 40% of b = 40/100 *b = 4b/10
New value after this change = b - 40% decreased value of b = b -4b/10
= (10b-4b)/10 = 6b/10
Step 2 The new value obtained is again decreased by 40%
value of 40% number found in step 1 = 40% of value found in step 1
value of 40% number found in step 1 = 40/100 * 6b/10 = 24b/100
This value (24b/100) is subtracted from value found in step 1(6b/10) as given that value obtained is decreased by 40%
new value found after 40% decrease = 6b/10 - 24b/100
new value found after 40% decrease = 60b/100 - 24b/100= 36b/100
new value found after 40% decrease = 36b/100 = 9b/25
Thus, the result of b is decreased by 40% and decreased again by 40% is 9b/25
Solve the initial-value problem. x' + 2tx = 5t, x(0) = 8 x(t) =
Multiply both sides of the ODE
[tex]x'+2tx+5t[/tex]
by [tex]e^{t^2}[/tex]:
[tex]e^{t^2}x'+2te^{t^2}x=5te^{t^2}[/tex]
Now the left side can be condensed as the derivative of a product:
[tex]\left(e^{t^2}x\right)'=5te^{t^2}[/tex]
Integrate both sides, then solve for x :
[tex]e^{t^2}x=\dfrac52e^{t^2}+C[/tex]
[tex]\implies x(t)=\dfrac52+Ce^{-t^2}[/tex]
Given that x(0) = 8, we find
[tex]8=\dfrac52+Ce^0\implies C=\dfrac{11}2[/tex]
so that the particular solution to this IVP is
[tex]\boxed{x(t)=\dfrac{5+11e^{-t^2}}2}[/tex]
The sugar content of the syrup in canned peaches is normally distributed. A random sample of n=25 cans yields a sample standard deviation of s=6.9 milligrams. Construct a 99% one-sided lower confidence bound for the population variance.
Answer:
99% one-sided lower confidence bound = 26.77
Step-by-step explanation:
We have to calculate a 99% one-sided lower confidence bound for the population variance.
The sample size is n=25.
The degrees of freedom are then:
[tex]df=n-1=25-1=24[/tex]
The critical value of the chi-square for this confidence bound is:
[tex]\chi^2_{0.01, \,24}=42.98[/tex]
Then, the lower confidence bound can be calculated as:
[tex]LB=\dfrac{(n-1)s^2}{\chi^2_{0.01,24}}=\dfrac{24\cdot(6.9)^2}{42.98}=\dfrac{1,142.64}{42.68}=26.77[/tex]
What is 66 tens +20 tens
Answer:
860.
Step-by-step explanation:
66 x 10= 660
20 x 10= 200
660+200= 860.
Answer:880
Step-by-step explanation:
[tex]66 x 10=66020 x 10=200200+660=880[/tex]
Solve for w. 5w + 9z = 2z + 3w
Answer:
w = -7z/2
Step-by-step explanation:
Our goal is to isolate w
1. subtract 3w from both sides to get 2w+9z = 2z
2. Subtract 9z from both sides to get 2w = -7z
3. Divide both sides by 2 to get w = -7z/2
We cannot simplify further, so this is our answer.
Which shapes have the same volume as the given rectangular prism?
base area = 50 cm^2
Answer:The first one
Step-by-step explanation:
V rectangular prism = Area of the base *5
Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y) → (0, 0) x4 − 36y2 x2 + 18y2
Looks like the limit is
[tex]\displaystyle\lim_{(x,y)\to(0,0)}\frac{x^4-36y^2}{x^2+18y^2}[/tex]
Let [tex]y=x^m[/tex] with [tex]m\ge1[/tex], so the limit is equivalent to
[tex]\displaystyle\lim_{x\to0}\frac{x^4-36x^{2m}}{x^2+18x^{2m}}=\lim_{x\to0}\frac{x^2-36x^{2(m-1)}}{1+18x^{2(m-1)}}=0[/tex]
Now let [tex]x=y^n[/tex] with [tex]n\ge1[/tex], so the limit is
[tex]\displaystyle\lim_{y\to0}\frac{y^{4n}-36y^2}{y^{2n}+18y^2}=\lim_{y\to0}\frac{y^{2(2n-1)}-36}{y^{2(n-1)}+18}=-\dfrac{36}{18}=-2[/tex]
The value of the limit evidently depends on path of approach, so the limit does not exist.
A girl loves to receive mail, but only 5% of the family's letters are addressed to her. The recipient of each letter is independent of all other letters. Find the mean number of letters received by other members of the family prior to her receiving her second letter.
Answer:
Negative Binomial
Step-by-step explanation:
The girl receives only 5% of mail which are addressed to her. Rest of 95% mails belong to other family members.
P (X) = 5%
P (X) = 95 / 5
P (X) = 19
The family receives 19 mails out of which only 5% will address the girl. The all other mails belong to the other family members.
HELP ON THIS QUESTION PLEASE
Answer:
slope is m=1. y-intercept is -1
Answer:
Slope is 1 and intercept is -1. Slope can be found by taking the rise and run of 2 points on a graph. and intercept is just when x = 0
The height of the triangle is
The base of the triangle is
The area of the triangle is
Answer:
The height of triangle is 12cm.
The base of triangle is 25 cm.
The area of triangle is 150cm².
Step-by-step explanation:
Given that the area of triangle is Area = 1/2×base×height. So you have to substitute the values into the formula :
[tex]area = \frac{1}{2} \times base \times height[/tex]
[tex]let \: base = 25 \\ let \: height = 12[/tex]
[tex]area = \frac{1}{2} \times 25 \times 12[/tex]
[tex]area = \frac{1}{2} \times 300[/tex]
[tex]area = 150 \: {cm}^{2} [/tex]
Evaluate. Write your answer as a fraction or whole number without exponents. 9^–3 =
Answer:
[tex]\frac{1}{9^3}[/tex] or [tex]\frac{1}{729}[/tex]
Step-by-step explanation:
When we have an exponent that is a negative, it is the same thing as 1 over the positive exponent. So, we move 9^-3 into 1/9^3 and then we evaluate the exponent to get our answer.
Pls help me with my geometry guys
Answer:
(1,1)
Step-by-step explanation:
x=1
y=1
6(1) + 1=7
6+1=7
Answer:
x=1, y=1
Step-by-step explanation:
Help!!! Type SSS, SAS, ASA,
AAS, or HL to justify
why the two larger
triangles are congruent.
DB = CA
its congruent by HL or RHSaxiom
Answer:
HL
Step-by-step explanation:
[tex] In\: right \triangle 's DAB \: \&\: CBA\\
\angle DAB \cong \angle CBA... (each 90\degree) \\ hypotenuse \: DB \cong hypotenuse \: CA. (given) \\
side AB \cong side BA.. (common) \\
\therefore \triangle DAB \cong \triangle CBA.. (By \: RHS\: or \: HL \: Postulate) [/tex]
The area of the parallelogram is____________________
the area of the quadrilateral.
What goes in the blank?
Answer:
double
Step-by-step explanation: