Help please on question 61!!

Answer:

x=62

Step-by-step explanation:

a triangle equals 180

so knowing that you subtract 56 from 180

That gives you 124

Then you divide it by 2 because the sides are equal.

That gives you 62

so x=62

Answer:

C is a function

Step-by-step explanation:

We can use the vertical line test.  If a vertical straight lines passes through the graph more than one, it is not a function

A and B are not functions

C is a function

Answer:

(a) 283 days

(b) 248 days

Step-by-step explanation:

The complete question is:

The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 268 days and a standard deviation of 12 days. ​(a) What is the minimum pregnancy length that can be in the top 11​% of pregnancy​ lengths? ​(b) What is the maximum pregnancy length that can be in the bottom ​5% of pregnancy​ lengths?

Solution:

The random variable X can be defined as the pregnancy length in days.

Then, from the provided information [tex]X\sim N(\mu=268, \sigma^{2}=12^{2})[/tex].

(a)

The minimum pregnancy length that can be in the top 11​% of pregnancy​ lengths implies that:

P (X > x) = 0.11

⇒ P (Z > z) = 0.11

⇒ z = 1.23

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\1.23=\frac{x-268}{12}\\\\x=268+(12\times 1.23)\\\\x=282.76\\\\x\approx 283[/tex]

Thus, the minimum pregnancy length that can be in the top 11​% of pregnancy​ lengths is 283 days.

(b)

The maximum pregnancy length that can be in the bottom ​5% of pregnancy​ lengths implies that:

P (X < x) = 0.05

⇒ P (Z < z) = 0.05

⇒ z = -1.645

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\-1.645=\frac{x-268}{12}\\\\x=268-(12\times 1.645)\\\\x=248.26\\\\x\approx 248[/tex]

Thus, the maximum pregnancy length that can be in the bottom ​5% of pregnancy​ lengths is 248 days.

Answer:

-8x + 12

Step-by-step explanation:

Distribute -4 to the parentheses:

-4(2x - 3)

-4(2x) = -8x

-4(-3) = 12

-8x + 12

Answer:

-8x +12

Step-by-step explanation:

-4(2x-3)

Distribute

-4* 2x -4 *-3

-8x +12

Answer:

67°

Step-by-step explanation:

CGE + AGC + AGG = 180 (angles on a straight line)

23°+90°+x=180°

x=67°

Answer:

Hey there!

The equation of all of these problems should be in slope-intercept, or, y=mx+b form.

In y=mx+b form, the m is the gradient, and y intercept is the b value.

a) y=2x+4

b) y=-2x-4

c) y=1x-1/5 (But as you may know, 1x=x, because one times any number is just that number, so we can actually have: y=x-1/5.)

d) y=-x+3.78

e) y=-2/3x+0 (Can be simplified to y=-2/3x)

f) y=0x-2/3 (Can be simplified to y=-2/3)

This can be confusing, especially if you're new to the topic. Let me know if you need more help :)

Answer:

22 units²

Step-by-step explanation:

1/2b*h=area

You can either count the units or use the distance formula.

[tex]d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]

b = 4 units

h = 11 units

area = (1/2*4)*11 = 22 units²

Answer:

{4, 5, 6}, {64, 65, 66}, {124, 125, 126}

Step-by-step explanation:

x = 1st number

x + 1 = 2nd number

x + 2 = 3rd number

{4, 5, 6}, {64, 65, 66}, {124, 125, 126}

The possible set of numbers are {4,5,6}, {64,65,66} and {124,125,126}

Consecutive numbers are the numbers which follow each other in order from small to greater number.

Let three consecutive numbers are, x ,x+1 and x+2.

According to given condition,

The first number is a multiple of 4,

The second number is a multiple of 5,

And The second number is a multiple of 6.

Start from 4 and then try to find out sequence,

The numbers can be 4, 5 and 6.

Further, the number can be 64,65 and66

And The numbers can be 124,125 and 126

So, three sets of numbers are {4,5,6}, {64,65,66} and {124,125,126}

To know more about Consecutive number on:

https://brainly.com/question/2493629

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the details :

Kofi is older than kweku

kofi's age = (5x-4) years

kweku's age = (2x+1) years

a. write down an expression, interns of x,for how much old is Kofi than kweku

Equate the ages of Kofi and kweku

(5x - 4) = (2x + 1)

5x - 4 = 2x + 1

5x - 2x = 1 + 4

3x = 5

3x - 5

B.) if Kofi is tens years older than kweku, find the value of x and the ages of Kofi and kweku

Then,

(5x-4) = (2x + 1) + 10

5x - 4 = 2x + 1 + 10

5x - 2x = 1 + 10 + 4

3x = 15

x = 5

Kofi's age : 5x - 4

5(5) - 4 = 25 - 4 = 21 years

Kweku's age : (2x + 1)

2(5) + 1 = 10 + 1 = 11 years

Answer:

1. No solution

2. Infinitely many solutions

3. Infinitely many solutions

4. One solution

Step-by-step explanation:

1.

x=y-3

2x-2y=6

Substitute x=y-3 in (2)

2(y-3)-2y=6

2y-6-2y=6

2y-2y=6+6

0=12

No solution

2.

5x+2y=-7

10x+4y=-14

Multiply (1) by 2 and (2) by 1

10x+4y=-14

10x+4y=-14

Subtract (3) from (4)

0+0=0

0=0

Infinitely many solutions

3.

y=2x+1

4x-2y=-2

Substitute y=2x+1 into (2)

4x-2(2x+1)=-2

4x-4x-2=-2

4x-4x=-2+2

0=0

Infinitely many solutions

4.

9x+6y=15

2y= -1+3x

From 2

2y+1-3x=0

-3x+2y=-1

9x+6y=15 (1)

-3x+2y=-1 (2)

Multiply (2) by 3

-9x+6y=-3

9x+6y=15

Subtract (3) from (1)

9x-(-9x)=15-(-3)

9x+9x=15+3

18x=18

x=18/18

=1

x=1

Substitute x=1 into (1)

9x+6y=15

9(1)+6y=15

9+6y=15

6y=15-9

6y=6

y=6/6

=1

One solution

Answer:

Step-by-step explanation:

-0.25z= -1.25

Convert the decimals to improper fractions

That's

So we have

Multiply through by 4

We have

- z = - 5

Divide both sides by - 1

the final answer is

Hope this helps you

Answer:

Step-by-step explanation:

[tex] \mathsf{ - 0.25z = - 1.25}[/tex]

Divide both sides of the equation by -0.25

[tex] \mathsf{ \frac{ - 0.25z}{ - 0.25} = \frac{ - 1.25}{ - 0.25} }[/tex]

Calculate

[tex] \mathsf{z = 5}[/tex]

Hope I helped !

Best regards!

Answer:

a) [tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]

b) (i) [tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]

   (ii) [tex]k=2[/tex]

Step-by-step explanation:

It is given that,

[tex]a=\begin{pmatrix}4\\-10\end{pmatrix},b=\begin{pmatrix}-2\\1\end{pmatrix},c=\begin{pmatrix}-4\\6\end{pmatrix}[/tex]

a)

We need to find the value of a+b+c.

[tex]a+b+c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-2\\1\end{pmatrix}+\begin{pmatrix}-4\\6\end{pmatrix}[/tex]

[tex]a+b+c=\begin{pmatrix}4+(-2)+(-4)\\-10+1+6\end{pmatrix}[/tex]

[tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]

b)

(i) We need to find the value of a+2c.

[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+2\begin{pmatrix}-4\\6\end{pmatrix}[/tex]

[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-8\\12\end{pmatrix}[/tex]

[tex]a+2c=\begin{pmatrix}4+(-8)\\-10+12\end{pmatrix}[/tex]

[tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]

(ii) It is given that a+2c=kb, where k is an integer. We need to find the value of k.

[tex]a+2c=k\begin{pmatrix}-2\\1\end{pmatrix}[/tex]

[tex]\begin{pmatrix}-4\\2\end{pmatrix}=\begin{pmatrix}-2k\\k\end{pmatrix}[/tex]

On comparing both sides, we get

[tex]k=2[/tex]

Answer:

C. the subtraction property of equality

Step-by-step explanation:

given

12 − x = 7x + 32

Subtract 12 from each side  using the subtraction property of equality

Step 1: -x = 7x + 20

Subtract -7x from each side using the subtraction property of equality

Step 2: -8x = 20

Answer:

$6291.70

Step-by-step explanation:

You have the equation and a value to solve for. So, plug this in to get m = 2500 + 0.05(75,834) = 2500 + 3791.70 = $6291.70.

Answer: 0.26

Step-by-step explanation:

As per given , we have

P(green tail) = 0.36

P(red fins) = 0.59

P(both a green tail and red fins ) = 0.21

Now, P(Neither red fin nor green tail )= 1 - P(either red fin or green tail )

[P(neither A nor B)= 1- P(either A or B)]

= 1-(P(green tail) +P(red fins)+P(both a green tail and red fins ))

[P(A or B)= P(A)+P(B)-P(A and B)]

= 1- (0.36+0.59-0.21)

= 1-(0.74)

= 0.26

Hence, the probability that the selected fish will not have a red fin or a green tail = 0.26

Answer: 14 units^2

Step-by-step explanation: 2 times 3 is 6, 2 times 4 is 8, 6+8=14.

Answer: 54.29%

Step-by-step explanation:

Given: The probability that they  will win both games is 38%.

i.e. P( both games will win) =0.38

The probability that they will win just the first game is  70%.

P(first game will win) = 0.70

To find : P(second game will win| first game will win)

Using formula: [tex]P(B|A)=\dfrac{P(\text{both A and B})}{P(A)}[/tex]

So, P(second game will win| first game will win) = [tex]\dfrac{\text{ P( both games will win)}}{\text{P(first game will win)}}[/tex]

[tex]=\frac{0.38}{0.70}\approx0.5429=54.29\%[/tex]

Hence, the required probability = 54.29%

Answer:

2m - 3

Step-by-step explanation:

We know that Jim ran m miles. Twice that amount is simply 2 times that, or 2 * m which simplifies to 2m. 3 miles fewer means that we have to subtract 3 from that quantity, so the answer is 2m - 3.

Answer:

2m - 3

Step-by-step explanation:

Distance ran by Jim = m

Twice as far as Jim : 2 * m = 2m

3 miles fewer than '2m' = 2m - 3

Distance ran by Kelly = 2m - 3

Answer:

2x²-32 ⇒ x²=16⇒ (-4,4)

4x²-100 ⇒x²=25 ⇒(-5,5)

x²-55=9 ⇒x²=64 ⇒(-8,8)

x²-140=-19 ⇒x²=121 ⇒(-11,11)

2x²-18=0 ⇒x²=9 ⇒(-3,3)

Answer:

Step-by-step explanation: Further explanation

[tex]2x^2-32=0\\\\\mathrm{Add\:}32\mathrm{\:to\:both\:sides}\\\\2x^2-32+32=0+32\\\\2x^2=32\\\\\frac{2x^2}{2}=\frac{32}{2}\\\\\mathrm{For\:}x^2=f\left(a\right)\\\\\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{16},\:x=-\sqrt{16}\\\\x=\sqrt{16},\:x=-\sqrt{16}\\x=4,\:x=-4[/tex]

[tex]4x^2-100=0\\\mathrm{Add\:}100\mathrm{\:to\:both\:sides}\\4x^2-100+100=0+100\\4x^2=100\\\frac{4x^2}{4}=\frac{100}{4}\\x^2=25\\\mathrm{For\:}x^2=f\left(a\right)\\\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\x=\sqrt{25},\:x=-\sqrt{25}\\\\x=5,\:x=-5[/tex]

[tex]x^2-140=-19\\x^2-140+140=-19+140\\x^2=121\\\mathrm{For\:}x^2=f\left(a\right)\\\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\x=\sqrt{121},\:x=-\sqrt{121}\\x=11,\:x=-11[/tex]

[tex]x^2-55=9\\x^2-55+55=9+55\\x^2=64\\\mathrm{For\:}x^2=f\left(a\right)\\\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\x=\sqrt{64},\:x=-\sqrt{64}\\x=8,\:x=-8\\[/tex]

[tex]2x^2-18=0\\2x^2-18+18=0+18\\2x^2=18\\\frac{2x^2}{2}=\frac{18}{2}\\x^2=9\\\mathrm{For\:}x^2=f\left(a\right)\\\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\x=\sqrt{9},\:x=-\sqrt{9}\\x=3,\:x=-3[/tex]

Answer:

x=-2.2 y=-1.6

Step-by-step explanation:

8x+y=-16

-3x+y=5

5x=-11

x=-11/5 or -2.2

-3x+y=5

-3(-2.2)+y=5

6.6+y=5

-6.6+y=-6.6

y=-1.6

Answer:

(−1, −8)

Step-by-step explanation:

(8x+y=−16)−1(−3x+y=−5)Becomes:8x+y=−163x−y=5Add these equations to eliminate y:11x=−11Then solve11x=−11for x:11x=−1111x11=−1111(Divide both sides by 11)x=−1

Now that we've found x let's plug it back in to solve for y.Write down an original equation:8x+y=−16Substitute−1forxin8x+y=−16:(8)(−1)+y=−16y−8=−16(Simplify both sides of the equation)y−8+8=−16+8(Add 8 to both sides)y=−8

Answer:

17

Step-by-step explanation:

Answer:

U B = 100.5

Step-by-step explanation:

the upper bound of the size of the television screen= 95.5 since it is corrected to the nearest 5 then the U B =100.5 cm

The upper bound of the size of the television screen is 100.5 cm

The conversion of the size of the television screen to the nearest 5cm from the initial size of 95 cm is = 100 cm.

Now, the upper bound of the size of the television screen which is 100 is can be determined by the addition of a half value to 100 cm:

i.e.

= (1/2) + 100 cm

= 0.5 + 100 cm

= 100.5 cm

Therefore, we can conclude that the upper bound of the size of the television screen is 100.5 cm

Learn more about nearest value here:

https://brainly.com/question/16382026?referrer=searchResults

Answer:

Salary after 5 year(A) = $60,485 (Approx)

Step-by-step explanation:

Given:

Staring salary(P) = $43,125

Growth rate(r) = 7%

Number of year (n) = (6-1) = 5

Find:

Salary after 5 year(A)

Computation:

[tex]A=P(1+r)^n \\\\ A = 43125(1+0.07)^5 \\\\ A = 60485[/tex]

Salary after 5 year(A) = $60,485 (Approx)

Answer:

A = ± [tex]\sqrt{\frac{q+3g}{b^2} }[/tex]

Step-by-step explanation:

Given

b²A² - 3g = q ( add 3g to both sides )

b²A² = q + 3g ( divide both sides by b² )

A² = [tex]\frac{q+3g}{b^2}[/tex] ( take the square root of both sides )

A = ± [tex]\sqrt{\frac{q+3g}{b^2} }[/tex]

Answer:

Step-by-step explanation:

√324=18

√576=24

√704=26.532....

Answer:

True

Step-by-step explanation:

Given that:

M = 27, sample of n = 36 scores, µ = 30 and σ = 18.

The z score is used in statistics to determine by how many standard deviations the raw score is above or below the mean. If the z score is positive, the raw score is greater than the mean and if the z score is negative the raw score is less than the mean. The z score is given as:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Given that M = 27, this means that x = 27. Therefore:

[tex]z=\frac{x-\mu}{\sigma}\\\\for \ a\ sample\ size(n):z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\z=\frac{27-30}{18/\sqrt{36} } =\frac{-3}{3}=-1[/tex]

This sample mean corresponds to a z-score of z = –1.00.

Answer:

to find the mean add all numbers the divide by the ammount of numbers given

Step-by-step explanation:

ex: 1 , 2 , 3    

add:

1+2+3=6

divide:

6 / 3 = 2  

your mean is 2

all good?

Answer: to find the mean add up all numbers and divide them by the amount of numbers there and to find the median that is the middle number write it on a piece of paper and cross out the beginning and end till you get the to the middle that is your median

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

3x - 5 = 1

Adding 5 to both sides gives us:

3x - 5 + 5 = 1 + 5

3x = 6

Dividing the equation by 3 gives us:

3x / 3 = 6 / 3

x = 2

Answer:

x = 2 Hfizfifsits96eotst9s

Answer:

[tex]\boxed{D. y + 6 = -3(x - 2)}[/tex]

Step-by-step explanation:

Hey there!

Well given point,

(2,-6)

Point slope form is,

y - y1 = m(x - x1)

Plug in the given point

y + 6 = m(x - 2)

Plug in slope

y + 6 = -3(x - 2)

So choice D. y + 6 = -3(x - 2) is correct.

Hope this helps :)

Answer:

14.6

Step-by-step explanation:

It is given that,

The average weight of the top 5 fish caught at a fishing tournament was 12.3 pounds. From the attached figure, the weight of 5 fish are given. We need to find the weight of Wayne S. fish.

Average = sum of terms/no of terms

Let the weight of Wayne S. is x. So,

Here the sum of terms is x+12.8+12.6+11.8+9.7 and the number of terms is 5.

[tex]12.3=\dfrac{x+12.8+12.6+11.8+9.7}{5}\\\\61.5=x+12.8+12.6+11.8+9.7\\\\61.5=x+46.9\\\\x=14.6[/tex]

So, the weight of the heaviest fish is 14.6.