Not sure how to solve this

Answer:

P(0,4)

Q(2,0)

Step-by-step explanation:

We khow that both P and Q are lying in the line : 4x+2y=8

Answer:

segment I'm and segment ad

Answer:

The answer is B

Step-by-step explanation:

Answer:

[tex]sin(A+B)=-\dfrac{345}{377}[/tex]

Step-by-step explanation:

Given that:

[tex]sin(A)=-\dfrac{20}{29}\\cos(B)=\dfrac{12}{13}[/tex]

A is in 3rd quadrant and B is in 1st quadrant.

To find: sin(A+B)

Solution:

We know the Formula:

1. [tex]sin(A+B) = sinAcosB+cosAsinB[/tex]

2. [tex]sin^{2} \theta+cos^{2} \theta=1[/tex]

Now, let us find the values of cosA and sinB.

[tex]sin^{2} A+cos^{2} A=1\\\Rightarrow (\frac{-20}{29})^2+cos^{2} A=1\\\Rightarrow cos^{2} A=1- \dfrac{400}{941}\\\Rightarrow cos^{2} A=\dfrac{941-400}{941}\\\Rightarrow cos^{2} A=\dfrac{441}{941}\\\Rightarrow cos A=\pm \dfrac{21}{29}[/tex]

A is in 3rd quadrant, so cosA will be negative,

[tex]\therefore cos A=-\dfrac{21}{29}[/tex]

[tex]sin^{2} B+cos^{2} B=1\\\Rightarrow sin^{2} A+(\frac{12}{13})^2=1\\\Rightarrow sin^{2} B=1- \dfrac{144}{169}\\\Rightarrow sin^{2} B=\dfrac{169-144}{169}\\\Rightarrow sin^{2} B=\dfrac{25}{169}\\\Rightarrow sinB=\pm \dfrac{5}{13}[/tex]

B is in 1st quadrant, sin B will be positive.

[tex]sinB =\dfrac{5}{13}[/tex]

Now, using the formula:

[tex]sin(A+B) = sinAcosB+cosAsinB\\\Rightarrow -\dfrac{20}{29} \times \dfrac{12}{13}-\dfrac{21}{29}\times \dfrac{5}{13}\\\Rightarrow -\dfrac{20\times 12+21\times 5}{29\times 13} \\\Rightarrow -\dfrac{240+105}{29\times 13} \\\Rightarrow -\dfrac{345}{377}[/tex]

[tex]sin(A+B)=-\dfrac{345}{377}[/tex]

Answer:

49 people

Step-by-step explanation:

Take the amount of candy and divide by the amount in a serving

2 3/4 ÷ 1/18

Change to an improper fraction

(4*2+3)/4 ÷ 1 /18

11/4 ÷ 1/18

Copy dot flip

11/4 * 18/1

198/4

49.5

Round down since people do not want half a serving

49 people

Answer: 2 29/36

Step-by-step explanation:

Hey there! :)

Answer:

13 packages.

Step-by-step explanation:

Begin by finding the total area of this composite figure. Separate the figure into separate rectangles. Use the formula A = l × w to calculate the area of each:

Smaller rectangle:

Subtract 7 from 9 to find the width:

9 -7 = 2. Therefore:

2 × 2 = 4 ft².

Larger rectangle:

7 × 5 = 35 ft².

Add up the two areas to find the area of the entire figure:

4 + 35 = 39 ft².

If each package of tile covers 3 ft², simply divide to find the package of tiles needed:

39 / 3 = 13 packages.

Answer:13

Step-by-step explanation:

The 4 angles need to add to 360.

2 of them are 70

The other two need to equal 360-140 = 220

They are both the same so one angle needs to equal 220/2 = 110

Now find x:

X + 60 = 110

Subtract 60 from both sides:

X = 50. The answer is D

Answer:

to find the dimension I would get 3.6/4.5=x/70 amd u get 3.6*70=4.5x and u get 252=4.5x and x=56

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the width of logo printed on canvas = x inches

Dimensions are in proportion

[tex]\frac{70}{x}=\frac{3.6}{4.5}\\[/tex]

Cross multiply

70 * 4.5 = x * 3.6

x * 3.6 = 315

[tex]x=\frac{315}{3.6}\\\\=\frac{3150}{36}\\\\x=87.5inches[/tex]

Answer: 5/26

Step-by-step explanation: 6/13 x 5/12

Answer:

(A⋂B) U (A⋂C) = {d, e}

Step-by-step explanation:

U= {a,b,c,d,e,f,g,h}

A = {b,d,e}

B = {a,d,e}

C={a,c,f,g,h}

=> A⋂B = {d,e}

=> A⋂C = ∅

=> (A⋂B) U (A⋂C) = {d, e}

Answer:

x= -7

Step-by-step explanation:

from the table, the pair of x= -7 is f(x)= -3

based on the table on the left f(-7)= -3

Answer:

A    -7

Step by step explanation: I took the test

Answer:

Step-by-step explanation:

hello

[tex]\dfrac{1}{9}-y^2=(\dfrac{1}{3})^2-y^2=(\dfrac{1}{3}-y)(\dfrac{1}{3}+y)=\dfrac{(1-3y)(1+3y)}{9}[/tex]

hope this helps

Answer:

1/5

Step-by-step explanation:

Gradient is another word for slope. To find the gradient, we have to use a formula.

Answer:

Explained below.

Step-by-step explanation:

Histogram is a graphical display of the data provided where the height of the bars represents the frequency of the values in a specific range.

The histograms can be used to draw conclusions about the shape of the distribution of the data provided.

In the histogram, if maximum of the data-values are collected on the left of the chart then the distribution is positively skewed.

In the histogram, if maximum of the data-values are collected on the right of the chart then the distribution is negatively skewed.

The frequencies provided can be converted into relative frequencies to determine what percentage of data is within a specific interval.

[tex]\text{Relative Frequency}=\frac{\text{Frequency of the group}}{N}\times100\%[/tex]

The formula of median is:

[tex]m = L + \left( \frac{\frac{N}{2} - F}{f}\right)C.[/tex]

Here,

L = lower class boundary of the group containing the median

N = total number of values

F = cumulative frequency of the groups before the median group

f = frequency of the median group

C = group width

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

The independent variables are the input values which are not dependent on the other value.

The dependent variables are the output values whose values depends on the value of some other number.

The independent variable in this case is the data on the set of distances she measured out.

The dependent variable in this case is the the time (measured by the stopwatch) it takes for the ball to roll.

The control variable in this case study is the size of ball, slope of hill, weight of ball etc.

Answer:

A

Step-by-step explanation:

Two congruent chords in a circle have the same distance from the center.

If two chords in a circle are congruent, then they are the same distance from the center of the circle .

The properties of Equal Chords of a Circle are:

According to the question

If two chords in a circle are congruent, then they are

Now,

By properties of Equal Chords of a Circle

The equal chords will be equal distance from the center of the circle .

Hence, If two chords in a circle are congruent, then they are the same distance from the center of the circle .

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Answer:

y=15; y=5

Step-by-step explanation:

y=x2+2x

plug in x as 3:

y=3 2+ 2*3

y=9+6

y=15

Next problem:

y=x3-3

plug in x as 2:

y=2 3-3

y=8-3

y=5

Answer:

4. ± 3.012

Step-by-step explanation:

Hello!

Assuming that for both variables X₁ and X₂ n₁= n₂ = 16

You need to test at 1% if the variable is significant, this means, if the slope for X₁ is different from zero (β₁≠0) using the t-statistic and the critical value approach.

The hypotheses are:

H₀: β₁= 0

H₁: β₁≠ 0

α: 0.01

[tex]t= \frac{b_1-\beta_1}{Sb_1} ~t_{n_1-3}[/tex]

The degrees of freedom "n₁-3" are determined by the number of parameters that you estimate for the multiple regression, in this case there are three "β₁" "β₂" and "δ²e"

The rejection region for this test is two-tailed, the critical values are:

±[tex]t_{n-3;1-\alpha /2}= t_{13;0.995}= 3.012[/tex]

I hope this helps!

Answer:

"30 years or less when, in reality, the average age is more than 30 years"

Step-by-step explanation:

Type I error is produced when conclusion rejects a true null hypothesis.

The null hypothesis is

"The average gamer is more than 30 years old"

(deduced from the wording, not explicitly stated).

Then if the conclusion is "the average gamer is less than or equal to 30 years old" when in reality the average age is more than 30 years, then there is a type I error, since the null hypothesis is rejected.

Answer is D:

"30 years or less when, in reality, the average age is more than 30 years"

Answer:

The discount is 36 dollars

The sale price is 44 dollars

Step-by-step explanation:

First find the discount by multiplying the original price by the discount rate

80*45%

Change to decimal form

80*.45

36

The discount is 36 dollars

The sale price is the original price minus the discount

80-36

44

The sale price is 44 dollars

Answer:

[tex]\dfrac{65}{81}[/tex] or 80.25%

Step-by-step explanation:

Number of blue Marbles = 4

Number of Red Marbles = 5

Total Number of marbles =4+5=9

[tex]P(B)=\dfrac49\\\\P(R)=\dfrac59[/tex]

In the experiment, two marbles are chosen one after the other with replacement.

The possible outcomes are: BB, BR, RB and RR

The probability of getting at least 1 red

=P(BR or RB or RR)

=P(BR)+P(RB)+P(RR)

[tex]=\left(\dfrac49\times\dfrac59\right) + \left(\dfrac59\times\dfrac49\right)+\left(\dfrac59\times\dfrac59\right)\\\\=\dfrac{20}{81}+\dfrac{20}{81}+\dfrac{25}{81}\\\\=\dfrac{65}{81}[/tex]

Expressed as a percentage, we have:

[tex]\dfrac{65}{81}\times100=80.25\%[/tex]

The probability of getting at least 1 red is 80.25%.

Answer:

[tex](x-(3+\sqrt5))[/tex] or [tex](x-3-\sqrt5)[/tex] is a factor of the given polynomial.

Step-by-step explanation:

Let us learn the concept with an example first.

Let the polynomial be a quadratic function [tex]g(x)[/tex].

[tex]g(x) = x^{2} -5x+6[/tex]

The roots of [tex]g(x)[/tex] are 2 and 3.

Putting [tex]x= 2\ in \ g(x)[/tex]

[tex]2^2-5\times 2+6 = 4-10+6 =0[/tex]

Putting [tex]x= 3\ in \ g(x)[/tex]

[tex]3^2-5\times 3+6 = 9-15+6 =0[/tex]

Putting x = 2 or x = 3, g(x) = 0 [tex]\therefore[/tex] The roots of equation g(x) are 2 and 3.

Now, let us try to factorize g(x):

[tex]x^{2} -2x-3x+6\\\Rightarrow x(x -2)-3(x-2)\\\Rightarrow (x-3)(x-2)[/tex]

so, the equation can be written as:

[tex]g(x) = x^{2} -5x+6=(x-3)(x-2)[/tex] where 3 and 2 are the roots of equation.

The factors are (x-3) and (x-2).

[tex]\therefore[/tex] for the polynomial f(x) which has roots [tex]3+\sqrt5\ and\ -6[/tex] will have a factor:

[tex](x-(3+\sqrt5))[/tex] or [tex](x-3-\sqrt5)[/tex]

Answer:

its its 12.

Step-by-step explanation:

=8÷4×6+2-2

=2×6+2-2

=12+2-2

=14-2

=12 is answer..

Answer:

12

Step-by-step explanation:

8÷4×6+2-2

=2×6+2-2

=12+2-2

14-2

=12

Answer:

  -5

Step-by-step explanation:

The value of x that gives f(x) = 3 is -5.

  [tex]f^{-1}(3)=-5[/tex]

Answer:

15

Step-by-step explanation:

PEMDAS

3x3 = 9

3+3 = 6

9+6 = 15

By the BODMAS rule we get, 3 + 3 × 3 + 3 =​ 15

The acronym BODMAS rule is used to keep track of the right sequence of operations to do when solving mathematical issues. Brackets (B), order of powers or roots (O), division (D), multiplication (M), addition (A), and subtraction (S) are all represented by this acronym (S).

3 + 3 × 3 + 3 =​

3 × 3 = 9

3 + 9 + 3 = 15.

Therefore, the correct answer is 15.

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Answer:

a) 10*0.51^3*0.49^2=approx 0.32

b)1-0.49^5= approx 0.97

c)1-0.51^5=0.965

d) approx 0.028 =P(all kids are girls)   approx 0.035 =P(all kids are boys)

P(all kids are of the same sexboys or girls)=0.063

Step-by-step explanation:

a) The probability that exactly 3 of 5 kids are boys is

p(3 boys)=C5 3 *p^3*q^2

C5 3 =   5!/(3!*2!)= 4*5/2=10

p=0.51 is the probability a child is boy

q=1-p=1-0.51=0.49 is the probability a child is girl

P(3 boys of 5 kids)= 10*0.51^3*0.49*2

b) The event that at least 1 kid from five is boy is a combination of events

1 boy -4 girls, 2 boys-3 girls, 3 boys-2 girls, 4 boys-1 girl, 5 boys.

The event " all 5 kids are the girls"  is the only event which is not the part of

event " at least 1 kid from five is boy"

So P(at least 1 kid from five is boy)=1 - P(all 5 kids are the girls)

P(all 5 kids are the girls)=0.49^5=approx 0.028

P(at least 1 kid from five is boy)=1-0.028=approx 0.97

c) Similarly like b)  P(at least one of five kids is girl)= 1-P(all 5 kids are the boys)

P(all 5 kids are the boys)=0.51^5=approx 0.035

P(at least one of five kids is girl)= 1-0.035=approx=0.965

d) Probability all kids are of the same sex= probability that all kids are the boys+ probability all kids are the girls.

Using b) and c)  P(all kids of the same sex)= 0.035+0.028=0.063

The probability that a family of five children has all children of the same gender is 0.06274.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

Given the probability of a child being a boy is 0.51, therefore, p= 0.51. Also, we can write the probability of the child not being a boy is 0.49(1-0.51), therefore, the probability of the child being a girl is 0.49 and q=0.49.

A.) The probability that a family of five children is exactly three boys can be written as

[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=3)= ^5C_3 \cdot (0.51)^3 \cdot (0.49)^{2}\\\\P(x=3) = 0.3184[/tex]

B.) The probability that a family of five children has at least one boy can be written as,

Probability of at least one boy = 1 - Probability of no boy

[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=0)= ^5C_0 \cdot (0.51)^0 \cdot (0.49)^{5}\\\\P(x=0) = 0.02824[/tex]

Now,

[tex]\text{Probability of at least one boy }= 1 - \text{Probability of no boy}\\\\P(x > 1) = 1-P(x=0)\\\\P(x > 1) = 1-0.02824 = 0.9717[/tex]

C.) The probability that a family of five children has at least one girl can be written as,

Probability of at least one girl= 1 - Probability of no girl

[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=5)= ^5C_5 \cdot (0.51)^5 \cdot (0.49)^{0}\\\\P(x=5) = 0.0345[/tex]

Now,

[tex]\text{Probability of at least one girl}= 1 - \text{Probability of no girl}\\\\P(x < 5) = 1-P(x=5)\\\\P(x > 1) = 1-0.0345= 0.9654[/tex]

D.) The probability that a family of five children has all children of the same gender can be written as,

Probability = Probability of all boys + Probability of all girls

[tex]P = P(x=0)+P(x=5)\\\\P = 0.02824+ 0.0345\\\\P= 0.06274[/tex]

Hence, The probability that a family of five children has all children of the same gender is 0.06274.

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Answer:

с.ifyt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to 70/g

Step-by-step explanation:

The given options

a.ifyt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to g 70

b. if yt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to 70/1

с.i fyt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to 70/g  

d. if yt grows at a rate of g percent per year, then the number of years it takes yt to triple is approximately equal to 70/g  

е.ifyt grows at a rate of g percent per year, then the number of years it takes yt to double is exactly equal to 70/g

The rule of 70 refers to the time period in which the investment you make is doubled. It analyzed that in how many years it took for doubling the amount by considering the specific rate of return  

Now we go through the options and as we can see that the option c meets the requirement as the g represents the growth rate and it fits to the above explanation

Answer:

The fire is 752.741 meters far from the base of tower

Step-by-step explanation:

Tower=160 meters tall

Angle of Depression=12°

tan(12°)=[tex]\frac{perpendicular(tower)}{base(distance from fire)}[/tex]

tan(12°)=[tex]\frac{160 meters}{base(distance from fire)}[/tex]

Distance from fire= [tex]\frac{160 meters}{tan12}[/tex]

Distance= 752.741 meters

Answer:

(1, 4) and (1,3), because they have the same x-value

Step-by-step explanation:

For a relation to be regarded as a function, there should be no two y-values assigned to an x-value. However, two different x-values can have the same y-values.

In the relation given in the equation, the ordered pairs (1,4) and (1,3), prevent the relation from being a function because, two y-values were assigned to the same x-value. x = 1, is having y = 4, and 3 respectively.

Therefore, the relation is not a function anymore if both ordered pairs are included.

The ordered pairs which make the relation not to be a function are: "(1, 4) and (1,3), because they have the same x-value".