Use completing the square to solve the equation x^2+16x=-44.

Answer:

19

Step-by-step explanation:

7 supersricpt 8

Answer:

Margin of Error = ME =± 5.2592

Step-by-step explanation:

In the given question n= 20 < 30

Then according to the central limit theorem z test will be applied in which the standard error will be  σ/√n.

Sample Mean = μ = 64

Standard Deviation= S= σ = 12

Confidence Interval = 95 %

α= 0.05

Critical Value for two tailed test for ∝= 0.05 = ±1.96

Margin of Error = ME = Standard Error *Critical Value

ME = 12/√20( ±1.96)=

ME    = 2.6833*( ±1.96)= ± 5.2592

The standard error for this test is σ/√n

=12/√20

=2.6833

Hey there! I'm happy to help!

We see that the father is 60 years old, and the son is half of that age, so this means that the son is 30 years old.

We want to see the age the son was at when the father was four times his age. We know that the father is thirty years older than him, so we can write this equation with s representing the age of the son.

s+30=4s   (30 years older than the son is equal to to four times the son's age at the time)

We subtract 30 from both sides.

s=4s-30

We subtract 4s from both sides.

-3s=-30

We divide both sides by -3.

s=10

Therefore, the boy was 10 when his father was four times his age. This is because his father would have been 40 because that is 30 more years than 10, and it is four times ten!

Have a wonderful day! :D

Answer:

Second Answer

Step-by-step explanation:

Answer:

(16x + 21) and (16x - 6)

Step-by-step explanation:

f(g(x)) = f(6 + 4x)

Applying the f(x) function on (6 + 4x) gives

4(6 + 4x) - 3

Which equals 16x + 24 - 3

= 16x + 21

g(f(x)) = g(4x - 3)

Applying the g(x) function on (4x - 3) gives

6 + 4(4x - 3)

Which equals 6 + 16x - 12

= 16x - 6

Answer:

(g∘f)(x)=48x2+48x+10

(g∘f)(x)=12x^2-6

Step-by-step explanation:

To find (f∘g)(x), use the definition of (f∘g)(x),

(f∘g)(x)=f(g(x))

Substituting 3x2−2 for g(x) gives

(f∘g)(x)=f(3x2−2)

Find f(3x2−2), where f(x)=4x+2, and simplify to get

(f∘g)(x)(f∘g)(x)(f∘g)(x)=4(3x2−2)+2=12x2−8+2=12x2−6

To find (g∘f)(x), use the definition of (g∘f)(x),

(g∘f)(x)=g(f(x))

Substituting 4x+2 for f(x) gives

(g∘f)(x)=g(4x+2)

Find g(4x+2), where g(x)=3x2−2, and simplify to get

(g∘f)(x)=3(4x+2)^2−2

(g∘f)(x)=48x2+48x+12−2

(g∘f)(x)=48x2+48x+10

Answer:

A:-4

Step-by-step explanation:

If you simplify 9(2x+1)<9x-18 you will get 9x<-27. That will mean x<-3 and the only answer for something less than -3 is -4.

If the answer was right, please put 5 stars.

Answer:

The answer would be-4

Step-by-step explanation:

Here,

9(2x+1) < 9x-18

or, 18x+9 < 9x-18

or, 18x-9x<-18-9

or, 9x<-27

or, x= -27/9

Therefore, the value of x is -4.

Hope it helps...

Answer:

C. 1/8

Step-by-step explanation:

Probability of shooting a goal on a throw is 2/4 = 1/2.

Probability of 3 in a row is (1/2)³ = 1/8.

Answer:

The meadian decreases by 1.5 when the outlier is removed.

Step-by-step explanation:

Well first we need to find the median of the following data set,

(75, 63, 58, 59, 63, 62, 56, 59)

So we order the set from least to greatest,

56, 58, 59, 59, 62, 63, 63, 75

Then we cross all the side numbers,

Which gets us 59 and 62.

59 + 62 = 121.

121 / 2 = 60.5

So 65 is the median before the outlier is removed.

Now when we remove the outlier which is 75.

Then we order it again,

56, 58, 59, 59, 62, 63, 63

Which gets us 59 as the median.

Thus,

the median height decreases by 1.5 units when the outlier is removed.

Hope this helps :)

Answer:

calls first evening = 26

calls second evening  = 80

calls third evening = 20

Step-by-step explanation:

Let x = calls third evening

x+6 = calls first evening

4x = calls second evening

x+6 + 4x + x = total calls = 126

Combine like terms

6x+6 = 126

Subtract 6 from each side

6x =120

Divide by 6

6x/6 =120/6

x = 20

x+6 = calls first evening = 20+6 = 26

4x = calls second evening = 4*20 = 80

Let x = calls third evening = 20

Answer:

y= 4.25x + $10

Step-by-step explanation:

A tool rental shop charges a flat fee of $10.00 to rent out their chain saw

An amount of $4.25 is charged for each of the days

Let x represent the amount that is charged for each day

Let y represent the total cost of the chain saw

Since the rental fee for each day is given as $4.25 and the flat fee is given as $10 then, the equation can be expressed as

y= $4.25x + $10

Hence the equation that expresses the cost y of renting this saw if it is rented for x days is y= $4.25x + $10

Answer:

Step-by-step explanation:

area = base x height

where base = 20 ft.

        height = ?

           area = 120 ft²

plugin values into the formula

120 = 20 x height

height = 120  

               20

height = 6 ft.

Answer:

[tex]\boxed{\sf k=6}[/tex]

Step-by-step explanation:

[tex]\sf kx (x-2)+6=0[/tex]

Expand brackets.

[tex]\sf kx^2 -2kx+6=0[/tex]

This is in quadratic form.

[tex]\sf ax^2 +bx+c=0[/tex]

Since this is for equal roots:

[tex]\sf b^2 -4ac=0[/tex]

[tex]\sf a=k\\b=-2k\\c=6[/tex]

[tex]\sf (-2k)^2 -4(k)(6)=0[/tex]

[tex]\sf 4k^2-24k=0[/tex]

[tex]\sf 4k(k-6)=0[/tex]

[tex]\sf 4k=0\\k=0[/tex]

[tex]\sf k-6=0\\k=6[/tex]

Plug k as 0 to check.

[tex]\sf \sf 0x^2 -2(0)x+6=0\\6=0[/tex]

False.

So that means k must equal 6.

Answer:

1.35

Step-by-step explanation:

next cube above 540 is 729

to get to 729: 729 / 540 = 1.35

n = 1.35

Answer:

The size square removed from each corner = 32.15 cm²

Step-by-step explanation:

The volume of the box = Length * Breadth * Height

Let r be the size  removed from each corner

Note that at maximum volume, [tex]\frac{dV}{dr} = 0[/tex]

The original length of the cardboard is 119 cm, if you remove a  size of r (This typically will be the height of the box)  from the corner, since there are two corners corresponding to the length of the box, the length of the box will be:

Length, L = 119 - 2r

Similarly for the breadth, B = 24 - 2r

And the height as stated earlier, H = r

Volume, V = L*B*H

V = (119-2r)(24-2r)r

V = r(2856 - 238r - 48r + 4r²)

V = 4r³ - 286r² + 2856r

At maximum volume dV/dr = 0

dV/dr = 12r² - 572r + 2856

12r² - 572r + 2856 = 0

By solving the quadratic equation above for the value of r:

r = 5.67 or 42

r cannot be 42 because the  size removed from the corner of the cardboard cannot be more than the width of the cardboard.

Note that the area of a square is r²

Therefore, the size square removed from each corner = 5.67² = 32.15 cm²

Answer:

Option D is correct.

Angle C = 70°

Step-by-step explanation:

The sum of angles in a triangle = 180°

So,

(Angle A) + (Angle B) + (Angle C) = 180°

(Angle A) = 67°

(Angle B) = 43°

(Angle C) = ?

67° + 43° + (Angle C) = 180°

Angle C = 180 - 67 - 43 = 70°

Angle C = 70°

Hope this Helps!!!

Answer:

see details below

Step-by-step explanation:

The price of a boat that Arthur wants is $29,450. Arthur finances this by paying $6000 down and monthly payment of $792.22 for 36 months.

a. Determine the amount to be financed.​​​​​​​15a. ___$23450____________

29450 - 6000 = 23450

b. Determine the installment price.​​​​​​​​b. ___$792,22______________

"monthly payment of $792.22"

c. Determine the finance charge.​​​​​​​​c. __$5069.92_______________

A = 792.22

n = 36

finance charge = total paid - amount to be financed

= 36*792.22 - 23450

= 5069.92

Answer:

15) 2.08m

Step-by-step explanation:

We kow tanA= p/b

Here, A=33°

b=3.2m

Then,

tan33°=p/3.2

0.65=p/3.2

p=0.65*3.2

p=2.08

So, The height of tree is 2.08m

14) 59.58ft

tan50°=p/b

1.19=p/50

p=59.58ft

So, The height of signpost is 59.58ft

In both of these problems, we will be using trigonometry! Remember, SOH-CAH-TOA.

14. x = 13.5950 ft

Visualization of the problem is attached below.

We want to find out the opposite side to the angle, and we know the adjacent side. Therefore, we should use the tangent function.

tan(50) = x / 50

x = tan(50) * 50

x = 13.5950 ft (round off wherever you need)

15. x = 241.0016 m

The visualization of the problem is already given. We know the same information as we need in the previous problems, an angle and an adjacent side, and we want to find the opposite side. Therefore, we should use the tangent function.

tan(33) = x / 3.2

x = tan(33) * 3.2

x = 241.0016 (round off wherever you need)

Hope this helps!! :)

Answer:

a

   $10,151   [tex]< \mu <[/tex]  $11448.12

b

  [tex]n = 158[/tex]

Step-by-step explanation:

From the question we are told that

    The  sample size is  n  =  19

    The  sample mean is  [tex]\= x =[/tex]$10,800

     The  standard deviation is  [tex]\sigma =[/tex]$1095  

    The  population mean is  [tex]\mu =[/tex]$225

Given that the confidence level is 99%  the level of significance is mathematically represented as

       [tex]\alpha = 100 -99[/tex]

      [tex]\alpha = 1[/tex]%

=>    [tex]\alpha = 0.01[/tex]

Now the critical values of [tex]\alpha = Z_{\frac{\alpha }{2} }[/tex] is obtained from the normal distribution table as

        [tex]Z_{\frac{0.01}{2} } = 2.58[/tex]

The reason we are obtaining values for [tex]\frac{\alpha }{2}[/tex] is because [tex]\alpha[/tex] is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while [tex]\frac{\alpha }{2}[/tex]  is the area under the normal distribution curve for just one tail and we need the  value for one tail in order to calculate the confidence interval

Now the margin of error is obtained as

     [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

    [tex]MOE = 2.58* \frac{1095 }{\sqrt{19} }[/tex]

     [tex]MOE = 648.12[/tex]

The  99% confidence interval for the population mean yearly premium is mathematically represented as

    [tex]\= x -MOE < \mu < \= x +MOE[/tex]

substituting values

   [tex]10800 -648.12 < \mu < 10800 + 648.12[/tex]

    [tex]10800 -648.12 < \mu < 10800 + 648.12[/tex]

   $10,151   [tex]< \mu <[/tex]  $11448.12

The  largest sample needed is mathematically evaluated as

      [tex]n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{\mu} ][/tex]

substituting values

       [tex]n = [ \frac{ 2.58 * 1095}{225} ]^2[/tex]

      [tex]n = 158[/tex]

Answer:

(A) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1 \geq \mu_2[/tex]    

     Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1<\mu_2[/tex]  

(B) The value of t-test statistics is -18.48.

(C) The P-value is Less than 0.005%.

(D) Reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

Step-by-step explanation:

We are given that the Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right;

Diet Regular

μ μ1 μ2

n 20 20

x 0.78062lb 0.81645 lb

s 0.00444 lb 0.00745 lb

Let [tex]\mu_1[/tex] = mean weight of contents of cans of diet soda.

[tex]\mu_2[/tex] = mean weight of contents of cans of regular soda.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1 \geq \mu_2[/tex]      {means that the contents of cans of diet soda have weights with a mean that is more than or equal to the mean for the regular soda}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1<\mu_2[/tex]     {means that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda}

The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;

                    T.S.  =  [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]  ~  [tex]t__n_1_+_n_2_-_2[/tex]

where, [tex]\bar X_1[/tex] = sample mean weight of cans of diet soda = 0.78062 lb

[tex]\bar X_2[/tex] = sample mean weight of cans of regular soda = 0.81645 lb

[tex]s_1[/tex] = sample standard deviation of cans of diet soda = 0.00444 lb

[tex]s_2[/tex] = sample standard deviation of cans of regular soda = 0.00745 lb

[tex]n_1[/tex] = sample of cans of diet soda = 20

[tex]n_2[/tex] = sample of cans of diet soda = 20

Also,  [tex]s_p =\sqrt{\frac{(n_1-1)s_1^{2}+ (n_2-1)s_2^{2}}{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(20-1)\times 0.00444^{2}+ (20-1)\times 0.00745^{2}}{20+20-2} }[/tex] = 0.00613

So, the test statistics =  [tex]\frac{(0.78062-0.81645)-(0)}{0.00613 \times \sqrt{\frac{1}{20}+\frac{1}{20} } }[/tex]  ~  [tex]t_3_8[/tex]

                                    =  -18.48

The value of t-test statistics is -18.48.

Also, the P-value of the test statistics is given by;

              P-value = P( [tex]t_3_8[/tex] < -18.48) = Less than 0.005%

Now, at a 0.01 level of significance, the t table gives a critical value of -2.429 at 38 degrees of freedom for the left-tailed test.

Since the value of our test statistics is less than the critical value of t as -18.48 < -2.429, so we have sufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda.

Answer:

Step-by-step explanation:

Simplify each term.

y ≤ −2x/5 + 2

Find the slope and the y-intercept for the boundary line.

Slope: -2/5

Y-intercept: 2

Graph a solid line, then shade the area below the boundary line since

y is less than -2x/5 + 2

y ≤ −2x/5 + 2

Hope this can help

Answer:

proper because the numerator is lower than the denominator

Answer:

72 degrees.

Step-by-step explanation:

The angle marked as 72 degrees and the angle of JOK are considered vertically opposite angles in relation to each other. This relationship means that the angles are equal.

Answer:

[tex]\boxed{Option \ C}[/tex]

Step-by-step explanation:

Congruent arcs subtend congruent central angles.

So,

∠GOH ≅ ∠JOK

∠JOK = 72 degrees

Answer:

2.09 seconds.

Step-by-step explanation:

We are given...

y = 70 feet

v0 = 0 feet/second

a = 32 feet/second^2

We need to find t using the following equation...

y = v0 * t + (1/2) * a * t^2

70 = 0 * t + (1/2) * 32 * t^2

70 = (1/2) * 32 * t^2

70 = 16t^2

16t^2 = 70

t^2 = 4.375

t = sqrt(4.375)

t = 2.091650066

So, it will take the toy about 2.09 seconds to hit the ground.

Hope this helps!

Answer:

2

Step-by-step explanation:

The degree of this polynomial is 2, since a parabola is drawn. A parabola is a graph of a quadratic equation which has the highest degree of 2.

Answer:

Hi! Answer will be below.

Step-by-step explanation:

The answer is 450.

If you divide 1.8 and 0.004 the answer you should get is 450.

Below I attached a picture of how to do long division...the picture is an example.

Hope this helps!:)

⭐️Have a wonderful day!⭐️

Answer: 1 30/39

Step-by-step explanation:

Because y/x=z and y/z=x are true with the same values, simply do 7 2/3 divided by 4 1/3 to get 69/39.

Hope it helps <3

Answer:

Step-by-step explanation:

In ACB and ECD

AC =~ CE [ Given ]

BC =~ CD [ Given ]

<ACD =~ <ECD [ Vertical angles ]

Hence, ∆ ACB =~ ECD by SAS congruency of triangles.

Then, <B = <D

In ∆ABC , sum of all three angles must be 180°

<A + <B + <C = 180°

plug the values

[tex] 30 + < d \: + 70 = 180[/tex]

Add the numbers

[tex]100 + < d = 180[/tex]

Move constant to R.H.S and change it's sign

[tex] < d = 180 - 110[/tex]

Subtract the numbers

[tex] < d = 80[/tex] °

Hope this helps..

Best regards!!

Answer:

a. H0 : p ≤ 0.11 Ha : p >0.11 ( one tailed test )

d. z= 1.3322

Step-by-step explanation:

We formulate our hypothesis as

a. H0 : p ≤ 0.11 Ha : p >0.11 ( one tailed test )

According to the given conditions

p`= 31/225= 0.1378

np`= 225 > 5

n q` = n (1-p`) = 225 ( 1- 31/225)= 193.995> 5

p = 0.4 x= 31 and n 225

c. Using the test statistic

z=  p`- p / √pq/n

d. Putting the values

z= 0.1378- 0.11/ √0.11*0.89/225

z= 0.1378- 0.11/ √0.0979/225

z= 0.1378- 0.11/ 0.02085

z= 1.3322

at 5% significance level the z- value is ± 1.645 for one tailed test

The calculated value falls in the critical region so we reject our null hypothesis H0 : p ≤ 0.11 and accept  Ha : p >0.11 and  conclude that the data indicates that the 11% of the world's population is left-handed.

The rejection region is attached.

The P- value is calculated by finding the corresponding value of the probability of z from the z - table and subtracting it from 1.

which appears to be 0.95 and subtracting from 1 gives 0.04998

Answer:

x ≥ 4

Step-by-step explanation:

Well to find the inequality we need to single out x,

4x - 1 ≥ 15

+1 to both sides

4x ≥ 16

Divide 4 by both sides

x ≥ 4

Thus,

x is greater than or equal to 4.

Hope this helps :)