Angle b= 50
Angle c= 130
Complementary angles are two angles that add to equal 90
Supplementary angles are two angles that add to equal 180
To find the measurement of angle b, subtract 40 from 90 (50)
To find the measurement of angle c, subtract 50 from 180 (130)
The measures of complementary and supplementary angles are given by m∠B = 50° and m∠C = 130°
What are Supplementary and Complementary Angles?Supplementary angles are two angles that add up to 180 degrees. In other words, if angle A and angle B are supplementary, then:
A + B = 180°
Complementary angles are two angles that add up to 90 degrees. In other words, if angle A and angle B are complementary, then:
A + B = 90°
Given data ,
If m∠A = 40°, then its complement ∠B = 90° - m∠A = 90° - 40° = 50°.
Since ∠C is a supplement of ∠B, we know that m∠C + m∠B = 180°.
Therefore, we can solve for m∠C by rearranging this equation to get:
m∠C = 180° - m∠B
Substituting the value we found for m∠B, we get:
m∠C = 180° - 50° = 130°
Hence , the angles are mZB = 50° and mZC = 130°.
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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
Does this table represent a function? Why or why not?
х
y
0
4
7
8
5
5
8
8
10
9
A. No, because two of the y-values are the same.
B. Yes, because there are two x-values that are the same,
C. Yes, because every x-value corresponds to exactly one y-value.
D. No, because one x-value corresponds to two different y-values.
Answer:
no because one x value corresponds to two different y values
A dinner at a restaurant was advertised at $60 plus 18% tax. The total bill for this dinner was. Show working plss
Answer:
Total bill = $70.80
Step-by-step explanation:
$60 × 0.18 = $10.80
$60 + $10.80 = $70.80
Hope this helps! :)
Answer:
$70.8
Step-by-step explanation:
Since it is 18 percent tax,we need to find 18% of 60$.In order to do that we need to do 60/1 mutiplied by 18/100 and doing the math 18% of 60 =10.8
Now we have to add 60+10.8=$70.8
Thank you and I hope all you have an amazing day.Hope this helps you.Thank you.
What is the leading coefficient of a cubic polynomial that has a value of −208 when x=1, and has zeros of 5, 5i, and −5i?
Answer:
2
Step-by-step explanation:
We already have the zeros, so we can write the cubic polynomial in this general form:
[tex]y = a(x - x_1)(x - x_2)(x - x_3)[/tex]
Where:
[tex]x_1 = 5[/tex]
[tex]x_2 = 5i[/tex]
[tex]x_3 = -5i[/tex]
So we have that:
[tex]y = a(x -5)(x - 5i)(x + 5i)[/tex]
[tex]y = a(x -5)(x^2 + 25)[/tex]
To find the value of the leading coefficient 'a', we can use the point (1, -208) given:
[tex]-208 = a(1 -5)(1 + 25)[/tex]
[tex]-208 = a(-4)(26)[/tex]
[tex]a = -208 / (-104) = 2[/tex]
So the leading coefficient is 2.
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
Find the gradient of the line 2y = 8x + 1 =
. Find the y-intercept of the line 4y + 8x = -8 =
Does the point (1 ,12) lie on the line y = 3x + 8 ? =
Does the point (-2 ,10) lie on the line y = 14 + 2x ? =
Answer:
56 46 38 2 12
Step-by-step explanation:
BRAINLIEST ANSWER WINS! A satellite is to be put into an elliptical orbit around a moon as shown below. A vertical ellipse is shown surrounding a spherical object labeled, moon. The moon is a sphere with radius of 1000 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 953 km to 466 km.
Answer:
D. x²/1953² + y²/ 1466² = 1
Step-by-step explanation:
==>Given:
Radius of spherical moon = 1000km
Distance of satellite from moon surface = 953km to 466km
==>Required:
Derived equation of ellipse
==>Solution:
The formula for driving an equation of ellipse is given as:
x²/a² + y²/b² = 1
Where,
a = length of the semi-major axis, while,
b = length of the semi-major axis
Since we are told that the satellite distance to the surface of the moon varies from 953km to 466km, values of a and b is calculated by summing each length to the radius of the moon as follows:
a = radius of moon + the larger distance of the satellite = 1000+953 = 1,953km
b = radius of moon + the smaller distance of the satellite = 1000+466 = 1,466km
Thus, the equation of the ellipse would be:
x²/1953² + y²/ 1466² = 1
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:
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
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.
Single discount rate equavalent to a series of discounts 20% and 25% is
Answer:
The single discount rate equavalent is a discount of 40%.
Step-by-step explanation:
The multiplier for a increase of a% is 1 + a/100.
The multiplier for a decrease of b% is 1 - b/100.
Discount of 20%:
20% decrease:
1 - (20/100) = 1 - 0.2 = 0.8
Discount of 25%:
1 - (25/100) = 1 - 0.25 = 0.75
Series of discounts(20% and 25%):
0.8*0.75 = 0.6
1 - 0.6 = 0.4
The single discount rate equavalent is a discount of 40%.
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
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]
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
Evaluate the following:
Answer:
csc∅ = 25/7
sec∅ = 25/24
cot∅ = 24/7
Step-by-step explanation:
Cosecant (csc) is 1/sin∅ or hypotenuse over opposite
Secant (sec) is 1/cos∅ or hypotenuse over adjacent
Cotangent (cot) is 1/tan∅ or adjacent over opposite
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]
Work out percentage change to 2 decimal places when price of 97 is decreased to 90
Answer:
7.22?
Step-by-step explanation:
After the last ice age began, the number of animal species in Australia changed rapidly. The relationship between the elapsed time, t, in years, since the ice age began, and the total number of animal species, S year(t), is modeled by the following function: S year(t)=25,000,000⋅(0.78)t Complete the following sentence about the rate of change in the number of species in decades. Round your answer to two decimal places. Every decade, the number of species decays by a factor of
Answer:
Every decade, the number of species decays by a factor of 0.0834.
Step-by-step explanation:
Let be [tex]S(t) = 25,000,000\cdot 0.78^{t}[/tex], [tex]\forall t \geq 0[/tex]. The decay rate per decay is deducted from the following relation:
[tex]\frac{S(t+10)}{S(t)} = \frac{25,000,000\cdot 0.78^{t+10}}{25,000,000\cdot 0.78^{t}}[/tex]
[tex]\frac{S(t+10)}{S(t)} = 0.78^{t+10-t}[/tex]
[tex]\frac{S(t+10)}{S(t)} = 0.78^{10}[/tex]
[tex]\frac{S(t+10)}{S(t)} = 0.0834[/tex]
Every decade, the number of species decays by a factor of 0.0834.
Answer:
28% subtracted
Step-by-step explanation:
khan
Explain in your own words why a polynomial can’t be a quadratic if a= 0?
If [tex]a = 0[/tex], then [tex]y = ax^2+bx+c[/tex] turns into [tex]y = 0x^2+bx+c[/tex]. That [tex]0x^2[/tex] term goes away because it turns into 0, and adding 0 onto anything does not change the expression.
So [tex]y = 0x^2+bx+c[/tex] turns into [tex]y = bx+c[/tex] which is a linear equation (b is the slope, c is the y intercept). It is no longer a quadratic as quadratic equations always graph out a curved parabola.
As an example, you could graph out [tex]y = 0x^2+3x+4[/tex] and note how it's the exact same as [tex]y = 3x+4[/tex], both of which are straight lines through the two points (0,4) and (1,7).
How can (4x⁵/2x²)³ be solved in 2 different ways
We assume that we need to simplify the expression in two different ways.
Answer:
One way: Raise both, the numerator and denominator, to the third power, and then simplify the expression.
Second way: Simplify the terms inside parentheses, and then raise the result to the third power.
The result of both ways is the same: [tex] \\8x^{9}[/tex]
Step-by-step explanation:
One way
Raise both, the numerator and denominator, to the third power, and then simplify the expression:
[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]
[tex] \\ (\frac{64x^{5*3}}{8x^{2*3}})[/tex]
[tex] \\ (\frac{64x^{15}}{8x^{6}})[/tex]
[tex] \\ \frac{64}{8}\frac{x^{15}}{x^{6}}[/tex]
[tex] \\8x^{9}[/tex]
This is the first simplification.
Second way
Simplify the terms inside parentheses, and then raise the result to the third power.
[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]
[tex] \\ (\frac{4}{2}*\frac{x^{5}}{x^{2}})^{3}[/tex]
[tex] \\ (2*x^{5-2})^{3}[/tex]
[tex] \\ (2*x^{3})^{3}[/tex]
[tex] \\ (2^{3}*x^{3*3})[/tex]
[tex] \\ (8*x^{9})[/tex]
or [tex] \\ 8x^{9}[/tex].
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!!!
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.
Which expression has a positive value?
A - Negative 4 + (negative 5) (negative 6) divided by (negative 3)
B - 8 Left-bracket 10 divided by (2) (negative 2) Right-bracket
C - 3 (negative 64 divided by 8) + 25
D - Negative 2 (negative 5) (negative 3) divided by 10
Answer:
C - 3 (negative 64 divided by 8) + 25 =1
Step-by-step explanation:
Answer:
C is correct answer
Step-by-step explanation:
Consider the y-intercepts of the functions. f(x)= 1/5 [x-15] g(x)= (x-2)^2 The y-coordinate of the greatest y-intercept is..
Answer:
4
Step-by-step explanation:
I used Desmos
We will see that the y-intercept of g(x) is larger than the y-intercept of f(x).
How to find the y-intercepts?For a function y = f(x), the y-intercept is the value that takes y when we evaluate in x = 0.
So, for the first function:
[tex]f(x) = (1/5)*|x - 15|[/tex]
The y-intercept is:
[tex]f(0) = (1/5)*|0 - 15| = 15/5 = 3[/tex]
For the second function:
[tex]g(x) = (x - 2)^2[/tex]
The y-intercept is:
[tex]g(0) = (0 - 2)^2 = (-2)^2 = 4[/tex]
Then we can see that g(x) has a greater y-intercept than f(x).
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write the number name for 6782163 in international system
Answer:
Six Million Seven Hundred Eighty Two Thousand one hundred sixty three
Step-by-step explanation:
Hope it helps...Pls Mark as Brainliest!!
Answer:
Six Million Seven Hundred Eighty Two Thousand One Hundred and Sixty Three.
Step-by-step explanation:
6, 782, 163
Provided that the ACT scores are reasonably normally distributed with a mean of 18 and standard deviation of 6, what is the proportion of students with a score of 24 or higher
Answer:
0.158655253931 or 15.8%
Step-by-step explanation:
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
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]
Which of these numbers is prime? 13, 30, 49, 65, 87
Answer:
13
Step-by-step explanation:
factors of 13 : 1, 13
factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
factors of 49: 1, 7, 49
factors of 65: 1, 5, 13, 65
factors of 87: 1, 3, 29, 87
An amusement park has 20 rides. Ethan has enough time to ride 3 rides before the park closes. How many different ways could Ethan pick to ride the 3 rides? PLZZZZ HELLPPPP MEEEE
Answer:
20*19*18 = 6840
UNLESS...............
he is allowed to ride the same ride again , over and over....
then it is 20 x 20 x 20 = 8000
Step-by-step explanation: