Step-by-step explanation:
sin∠M = cos∠N
sin∠M = cos(30°)
sin∠M = √3 / 2
m∠M = 60° or 120°
If ∠M is acute, m∠M = 60°.
Answer: The measure of ∠M is 60°
Step-by-step explanation:
The complement of 30° is 60°
sin∠M =cos∠N
sin∠60°=cos∠30°
the measure of ∠M is 60°
A random sample of 11 students produced the following data, where x is the hours spent per month playing games, and y is the final exam score (out of a maximum of 50 points). The data are presented below in the table of values.
x y
14 46
15 49
16 37
17 42
18 37
19 31
20 25
21 23
22 20
23 15
24 12
What is the value of the intercept of the regression line, b, rounded to one decimal place?
Answer:
b = - 3.7
Step-by-step explanation:
here are the data values:
x y XY X²
14 46 644 196
15 49 735 225
16 37 592 256
17 42 714 289
18 37 666 324
19 31 589 361
20 25 500 400
21 23 483 441
22 20 440 484
23 15 345 529
24 12 288 576
now we are required to find the summation (total) of all values of X, Y, XY and X².
∑X = 209
∑Y = 337
∑XY = 5996
∑X² = 4081
The formular for finding b is given as:
b = n∑XY - (X)(Y) / n∑X² - (∑X)²
= 11(5996) - (209)(337) / 11(4081) - (209)²
= 65956 - 70433 / 44891 - 43681
= -4477/ 1210
= -3.7
The question asked us to find the value of b but we can go further to find the equation of the regression line:
a = ∑Y - b∑X / n
= 337 - (-3.7)(209)/ 11
=1110.3/11
= 100.94
the equation is:
Y = 100.94 - 3.7X
I hope you find my solution useful!
=
In a study of pain relievers, 50 people were given product A, and 35 experienced relief. In the same study, 25 people were given product B, and 19 experienced relief. Fill in the blanks of the statement below to make the statement the most reasonable possible. Product __ performed better in the study because __% got relief with this product, whereas only __% got relief from product __
Answer:
Product B performed better in the study because 76% got relief with this product, whereas only 70% got relief from product A
Step-by-step explanation:
Product A
Total number of people tested = 50
Total number o who experienced relief using product A
= 35
% of people who got relief using product A
= 35/50 x 100%
= 70%
Product B
Total number of people tested = 25
Total number of people who experienced releif using product B
= 19
% of peope who got relief using product B
= 19/25 x 100%
= 76%
From the above:
76% of people got relieved whilst using product B
70% who got relieved using product A.
Therefore, product B performed better in the study because 76% got relief with this product, whereas only 70% got relief from product A
Drag the ruler over each side of the triangle to find its length. The length of AB is . The length of BC is . ASAP Drag the protractor over each angle to find its measure. The measure of angle C is . The measure of angle B is .
Answer:
Drag the ruler over each side of the triangle to find its length.
The length of AB is
✔ 5
.
The length of BC is
✔ 4
.
Drag the protractor over each angle to find its measure.
The measure of angle C is
✔ 90°
.
The measure of angle B is
✔ 36.9°
.
Step-by-step explanation:
The length of sides AB and BC of the triangle will be 5 units and 4 units. And the measure of angle C and angle B of the triangle will be 90° and 37°.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Drag the ruler over each side of the triangle to find its length.
The length of side AB of the triangle is 5 units.
The length of side BC of the triangle is 4 units.
Drag the protractor over each angle to find its measure.
The measure of angle C of the triangle is 90°.
The measure of angle B of the triangle is 37°.
The length of sides AB and BC of the triangle will be 5 units and 4 units.
And the measure of angle C and angle B of the triangle will be 90° and 37°.
More about the right-angle triangle link is given below.
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Using only the confidence interval approach, at LaTeX: \alpha α = 0.05, the conclusion about the LaTeX: \beta β1 hypothesis test is:
Answer:
Reject the null hypothesis because the value of null is outside the interval.
Step-by-step explanation:
Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value Test statistics is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. In the given case p-value is less than critical value then we should reject the null hypothesis.
Suppose you are standing such that a 32-foot tree is directly between you and the sun. If you are standing 140 feet away from the tree and the tree casts a 160-foot shadow, how tall could you be and still be completely in the shadow of the tree? x 160 ft 140 ft 32 ft
Answer:
Height = 4 feet
Step-by-step explanation:
To determine how tall I can be we take the difference between the shadow cast by the 32-feet tree and the distance away from the tree
But the tree is 32 feet tall but on shadow it's 160
So lemme determine how long I'll be in my shadow first
Distance away from tree= 140 feet
Length of shadow cast by tree
= 160 feet
Length of shadow= 160-140
Length if shadow= 20 feet
My height= x
X/20= 32/160
X= 20*32/260
X = 4 feet
Height = 4 feet
Lauren bought 4 bags of popcorn for $3.00. What is the unit rate per bag of popcorn."?
Answer:
$0.75
Step-by-step explanation:
Given that
Number of bags of popcorn bought = 4
Total money spent = $3.00
To find:
Unit rate per bag of popcorn = ?
i.e. price of one bag of popcorn is to be find out.
Solution:
We can use ratio here to find the rate of one bag of popcorn.
4 bags bought at $3
4 bags : $3
Let us divide both the sides with 4.
[tex]\frac{4}4[/tex] bags : $ [tex]\frac{3}4[/tex]
OR
1 bag bought at $ 0.75
We can alternatively use unitary method.
4 bags are bought at $ 3
1 bag is bought at $ [tex]\frac{3}{4}[/tex]
1 bag is bought at $0.75.
So, unit rate per bag of popcorn is $0.75.
About 25% of young Americans have delayed starting a family due to the continued economic slump. Determine if the following statements are true or false, and explain your reasoning.a. The distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump in random samples of size 12 is right skewed.b. In order for the distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump to be approximatly normal, we need random samples where the sample size is at least 40.c. A random sample of 50 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.d. A random sample of 150 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.e. Tripling the sample size will reduce the standard error of the sample proportion by one-third.
Answer:
a. True
b. true
c. false
d. false
e. false
Step-by-step explanation:
a. true
polutation = 25% = 0.25
sample = n= 12
n x p
= 12 x o. 25 = 3 and 3 is less than 10
12(1 - p)
= 12 x 0.75
= 9 and is less than 10
b. True
the sample distribution of the population is normal when
sample size x population > or equal to 10
40 x 0.75
= 30 and 30 is greater than 10
c. false
50 x 0.25 = 12.5
50 x 0.20 = 10
z = 10 - 12.5/sqrt(12.5)
= -2.5/3.54
= -0.70
H0: Young american family who delayed
H1: young american family who did not delay
p(z = -0.70)
0.2420>0.005
therefore we accept the null hypothesis
d. false
150 x 0.20 = 30
150 x 0.75 = 37.5
z = 30 - 37.5/sqrt(37.5) = -7.5/6.12 = -1.22
p(z = -1.22) = 0.1112 > 0.05
therefore we do not reject the null hypothesis
e. false
se1 = sqrt(p(1-p)/n
se2 = sqrt(p(1-p)/3n
se2 = 1/sqrt(3)se2
if a salesman has a base salary of 35,000 per year makes 5% commission on each sales ,how much must he do in sales to make a total of 75,000 for the year
He must do a 8,00,000 sales to make total of 75000 for the year.
For salesman base salary = 35000, Salary to be atained is 75000. Having commission of 5% on every sales. Sales to be determine so the salesman attained 75000 for year.
In mathematics it deals with numbers of operations according to the statements.
Here, according to the statement.
Let x be sales,
35,000 + 5%x = 75,000
0.05x = 75000-35000
x = 40000/0.05
x = 8,00,000
Thus, he must do a 8,00,000 sales to make total of 75000 for the year
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Find the midpoint of the segment connecting (−1.8, 1.9) and (1.2, 2.7).
Answer:
(-0.3, 2.3)
Step-by-step explanation:
(-1.8+1.2)/2 = -0.3
(1.9+2.7)/2 = 2.3
Answer:
( - 0.3 , 2.3 )Step-by-step explanation:
Let the points be A and B
A ( - 1.8 , 1.9 ) ⇒( x₁ , y₁ )
B ( 1.2 , 2.7 )⇒ ( x₂ , y₂ )
Now, let's find the midpoint:
[tex] \mathsf{ (\frac{x1 + x2}{2} \: , \frac{y1 + y2}{2} )}[/tex]
Plug the values
[tex] \mathsf{ = (\frac{ - 1.8 + 1.2}{2} \: , \frac{1.9 + 2.7}{2} )}[/tex]
Calculate
[tex] \mathsf{ = ( \frac{ - 0.6}{2} \: , \frac{4.6}{2} )}[/tex]
[tex] \mathsf{ = (- 0.3 \:, 2.3)}[/tex]
Hope I helped!
Best regards!
Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 7exyz, (0, 0, 7)
Answer:
Full question is:
Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 7[tex]e^{xyz}[/tex] at a specified point (0, 0, 7)
Step-by-step explanation:
If we have a level surface, then it will give us
f(x,y,z) = x+y+z = 7[tex]e^{xyz}[/tex]. where f is the function of the x, y, and z coordinates.
Now let us calculate the ∇ gradient of f at point (0,0,7):
∇[tex]f|_{(0,0,7)}[/tex] = (fx,fy,fz) = (1−7yz[tex]e^{xyz}[/tex],1−7xz[tex]e^{xyz}[/tex],1−7xy[tex]e^{xyz}[/tex])[tex]|_{(0,0,7)}[/tex]
= (1, 1, 1)
We get the equation for the tangent plane A:
A: 1(x−0) + 1(y−0) + 1(z−7)=0
This can also be written as:
x+y+z = 7 ------------------------------------------------------------------(a)
The equation for the normal line B gives us :
L: (x,y,z) = (0,0,7) + t(1, 1, 1), t ∈ R --------------------------------(b)
5 STARS IF CORRECT! Can you find the value of an expression when values for x and y are given? Explain.
If the expression has only two variables [tex] x[/tex] and $y$, or if there's just one variable out of these two, then the answer is yes.
If the expression has more variables (other than X and y), then the answer is no.
Your friend Stacy has given you the following algebraic expression: "Subtract 20
times a number n from twice the cube of the number. What is the expression that your
friend is saying?
Answer:
Expression = 2n³ - 20n
Step-by-step explanation:
Find:
Expression
Computation:
Assume given number is 'n'
Cube of number = n³
Twice of cube = 2n³
Subtract number = 20n
Expression = 2n³ - 20n
Help please I need help as soon as possible!all answers are appreciated! Keisha tried to evaluate an expression step by step. 3+(−4)−7
Answer:
D no mistakes
Step-by-step explanation:
3+(-4)-7 is equal to 3-4-7=-8
Answer:0
Step-by-step explanation:
3+(-4)-7 when there are parenthesis around a negative number you flip it to positive and then 4+3-7=0
What is the length of the arc on a circle with radius 16 inches intercepted by a 45° angle?
Find the circumference:
Circumference = 2 x PI x radius:
Circumference = 2 x 3.14 x 16 = 100.48 inches.
A full circle is 360 degrees, a 45 degree angle is 1/8 of a full circle.
Arc length = 100.48 / 8 = 12.56 inches.
An economist is interested in studying the income of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the width of the 90% confidence interval
Answer:
The width is [tex]w = 282.8[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 50
The population standard deviation is [tex]\sigma = \$ 1000[/tex]
The sample size is [tex]\= x = \$ 15,000[/tex]
Given that the confidence level is 90% then the level of significance can be mathematically represented as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10 \%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{0.10 }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{0.10}{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.645 * \frac{1000 }{\sqrt{50 }}[/tex]
=> [tex]E = 141.42[/tex]
The width of the 90% confidence level is mathematically represented as
[tex]w = 2 * E[/tex]
substituting values
[tex]w = 2 * 141.42[/tex]
[tex]w = 282.8[/tex]
What is the product of 2p + q and -39 - 6p + 1?
0 -12p2 - 6pq – 4p - 32 + 1
O-12p2- 12pq + 2p – 392 +9
- gp² q² + 12pq - 2p + 9
12p2 + 12pq +2p + 302 + 9
Answer:
Option (2)
Step-by-step explanation:
In this question we have to find the multiplication of the two expressions.
(2p + q)(-3q - 6p + 1)
= 2p(-3q - 6p + 1) + q(-3q - 6p + 1) [By distributive property]
= -6pq - 12p²+ 2p - 3q² - 6pq + q
= -12p² - (6pq + 6pq) - 3q² + 2p + q
= -12p² - 12pq + 2p - 3q² + q
Therefore, Option (2) will be the correct option.
if Israel spends the most time on social media with an average of 11.1 and peru spends a total time of 8.3 how much more time does israel spend on social media than peru
Answer:
israel spends 2.8 more (units) than peru.
Step-by-step explanation:
11.1 - 8.3 = 2.8, so israel spends 2.8 (units), more on social media.
Evaluate the polynomial when x = 3 and y = - 8
x2 + y2 + xy
Work Shown:
Replace x with 3, replace y with -8. Use order of operations PEMDAS to simplify.
x^2 + y^2 + x*y
3^2 + (-8)^2 + 3*(-8)
9 + 64 - 24
73 - 24
49
Answer:
49
Step-by-step explanation:
We are given the polynomial:
[tex]x^2+y^2+xy[/tex]
We want to evaluate when x=3 and y= -8. Therefore, we must substitute 3 for each x and -8 for each y.
[tex](3)^2+(-8)^2+(3*-8)[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
Solve the parentheses first. Multiply 3 and -9.
3*-8=-24
[tex](3)^2+(-8)^2 + -24[/tex]
[tex](3)^2+(-8)^2-24[/tex]
Now, solve the exponents.
3^2= 3*3 =9
[tex]9+ (-8)^2 -24[/tex]
-8^2= -8*-8= 64
[tex]9+64-24[/tex]
Add 9 and 64
[tex]73-24[/tex]
Subtract 24 from 73
[tex]49[/tex]
The polynomial evaluated for x=3 and y= -8 is 49.
Question 2 of 10
What is the slope of the line x = 3?
Answer:
[tex]\boxed{\mathrm{U n d e f i n e d \ slope }}[/tex]
Step-by-step explanation:
x = 3 is a vertical line.
The slope of a vertical line is undefined.
The radius of a circle measures 5 inches A central angle of the circle measuring 12 radians cuts off a sector
What is the area of the sector?
Enter your answer as a simplified fraction in the box
area =
inches squared
Answer:
25/4 square inches
Step-by-step explanation:
The area of a sector of a circle is given by the formula ...
A = (1/2)r²θ
where r is the radius and θ is the central angle in radians.
For your sector, the area is ...
A = (1/2)(5 in)²(1/2) = 25/4 in²
pls help ill give you 20 points and only correct answers plsss
Answer:
C) Local Eats
Step-by-step explanation:
So this one is pretty simple in retrospect. Just some proportions
Food Queen) 3.60:6=.60:1 1 pound is 60 cents
Grocery Smart) $1/4:1/2= $1/2:1 $1/2=50 cents 1 pound is 50 cents
Fresh Farm) $3:4=$1.50:2=.75:1 1 pound is 75 cents
Local Eats) .49:1 1 pound is 49 cents
As you can see, the answer is C) Local Eats
Step 1:
First, let's convert all of the numbers on the numerator side to decimals. Food Queen, Fresh Farm, and Local Eats are already in decimals, but Grocery Smart is not. 1/4 is 25%, which is equal to 0.25.
Step 2:
We need to convert all the values to represent the price of one pound. To do that, we just divide as written.
Food Queen: 3.00 ÷ 6 = 0.50
Grocery Smart: 0.25 ÷ 0.5 = 0.50
Fresh Farm: 3.00 ÷ 4 = 0.75
Local Eats: 0.49
Our answer: C. Local Eats. $0.49
Barry’s pet turtle, Turtlelini, escaped from his backyard. Barry found Turtlelini by the creek and wanted to determine how far Turtlelini had walked. On the map, Barry’s house is 0.6 inch from the creek. If the scale on the map shows that 1.5 inches are equivalent to 0.8 mile, how far did Turtlelini walk, to the nearest tenth of a mile?
Answer:
On the map:
0.8 mile / 1.5 inches
= 0.533 mile / 1 inch
Total distance on the map:
0.6 inches
distance travelled in miles:
0.6 * 0.533 = 0.32 miles
please mark brainly if you want
Answer:
The answer is A = 0.3 mile
Step-by-step explanation:
I got it right in 2021.
How many variables terms are in the expression 3xcube y+5xsquare+y+9
Answer: Please Give Me Brainliest, Thank You!
2
Step-by-step explanation:
There are two variables here, X and Y
Diabetic patients have normally distributed cholesterol with mean 200 and standard deviation=10.
Find the percentage of patients whose cholesterol is between 198 mg/dL and
207 mg/dL ?
Answer:
The percentage of patients whose cholesterol is between 198 mg/dL and 207 mg/dL is 33.73%
Step-by-step explanation:
To calculate this proportion, we follow the probability route, using the z-score statistics
Mathematically;
z-score = (x-mean)/SD
from the question, mean = 200 and SD = 10
So for 198
z-score = (198-200)/10 = -2/10 = -0.2
For 207
z-score = (207-200)/10 = 7/10 = 0.7
So the probability we want to calculate is;
P(-0.2<z<0.7)
Mathematically this can be calculated as;
P(z<0.7) - P(z<-0.2)
We can calculate the required probability using the standard normal distribution table
P(-0.2<x<0.7) = 0.3373 from the standard distribution table
So it is this 0.3373 that we now convert to percentage and that is 33.73%
I need help on this question ASAP please?
Answer:
B.
Step-by-step explanation:
10c + 5 ≤ 45
10c ≤ 40
c ≤ 4
Since the inequality uses the less than or equal to sign, we use a shaded circle on the number line. Since c is less than or equal to 4, your answer will be B, since the line extends infinitely to the left of 4.
Hope this helps!
Answer:
B
Step-by-step explanation:
To get the answer, you need to simplify or re-write the equation given:
10c + 5 ≤ 45 = 10 × c + 5 - (45) ≤ 0Next, group the like terms together:
10c - 40Now, we can apply algebra to simplify the equation further:
(10c ÷ 10) ≤ (40 ÷ 10)c ≤ 4Now, look at your options. Only option B matches our equations. Therefore, B is the correct answer.
Stephen Curry's record during the 2017 - 2018 NBA final game is made up of 2-point shots and 3-points.
His total points scored for the final game was 45 points with 19 shots made. How many 2-point shots did
he make? How many 3-point shots did he make?
2-Pointers:
3-Pointers:
Answer:
x = 12 ( two points shots )
y = 7 ( three points shots )
Step-by-step explanation:
Let´s call "x" two points shots, and "y" three points shots, then
x + y = 19
2*x + 3*y = 45
We have to solve a two-equation system for x and y
y = 19 - x
2*x + 3 * ( 19 - x ) = 45
2*x + 57 - 3*x = 45
- x = 45 - 57
-x = - 12
x = 12
And y = 19 - 12
y = 7
Find the polynomial for the area.
The area is
Answer: ¹/₂( x² - 10y² + 10xy - xy )
Step-by-step explanation:
From the diagram area of the triangle = ¹/₂ ˣ base ˣ height
where the base = x + 10y and the height = x - y
Therefore putting these into the formula above
Area = ¹/₂ [( x + 10y )( x -y )]
= ¹/₂( x² - xy + 10xy - 10y²)units²
= ¹/₂( x² - 10y² + 10xy - xy )
Suppose a jar contains 18 red marbles and 38 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
Answer: 0.0993
Step-by-step explanation:
Since the jar contains 18 red marbles and 38 blue marbles, the total marbles will be:
= 18 marbles + 38 marbles
= 56 marbles
When 2 marbles are pull out at random at the same time, the probability that both are red will be:
= (18/56) × (17/55)
= 0.3214 × 0.3091
= 0.0993
Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window. H represents the height of the tree (in centimeters), t years since Renata moved in. H = 210 + 33t How fast does the tree grow? ANSWER centimeters per year.
Answer:
The tree grows 33cm per year
Step-by-step explanation:
Here in this question, we are interested in knowing how fast the growth of the tree is.
This is easily obtainable from the equation for the height of the tree.
Mathematically, the equation is given as;
H = 210 + 33t
Interpreting this, we can have 210 as the original height of the tree when Renata moved in, while the term 33 represents the growth per year.
So we can say the tree adds a height of 33 cm each year and this translates to the yearly growth of the tree
Which polynomial represents the sum below?
Answer:
The sum is represented by the polynomial:
[tex]5\,x^9+2 \,x^7+13\,x+4[/tex]
Step-by-step explanation:
Recall that polynomials are added by combining like terms. The only like terms in this addition are: 5 x and 8 x which added render: 13 x. therefore, the addition of these polynomials renders;
[tex]5\,x^9+2 \,x^7+13\,x+4[/tex]
