A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the floor and 32 inches high. Sketch and find the equation describing the shape of the door. If you are 22 inches tall, how far must you stand from the edge of the door to keep from hitting your head?

Answer:

It  was gained 4 1/4 points.

Step-by-step explanation:

- 7 1/8 - 1 5/8 + 13 = - 8 6/8 + 13 = - 8 3/4 + 13 = - 8 - 3/4 + 12 + 4/4 =  4 1/4

Answer:  4.4 seconds

Step-by-step explanation:

h(t) = -16t² + 315

Since we want to find the total time the baseball is in the air, we need to find the time (t) when the ball lands on the ground --> h(t) = 0

  0  = -16t² + 315

-315 = -16t²

[tex]\dfrac{315}{16}=t^2\\\\\\\sqrt{\dfrac{315}{16}}=t\\\\\\\dfrac{\sqrt{315}}{4}=t\\\\\\\large\boxed{4.4=t}[/tex]

Answer:

≈ 4.44 sec

Step-by-step explanation:

h= 315 ft

h= 16t²

315 = 16t²

t²=315/16

t=√315/16 ≈ 4.44 sec

Answer:

576 for the week

Step-by-step explanation:

First determine how many hours she worked

4/5 * 40 = 32 hours

32 hours times the hourly rate of 18

32*18 =576

Answer :

I have solved for the points.

Explanation :

Just get a protractor and plot out the angles into a circle. Starting with the largest angle.

Answer:

{-1, -8}

Step-by-step explanation:

Please enclose "1 - 3x" inside parentheses so the reader will know that you want the square root of all of "1 - 3x".

Squaring both sides of the given equation, we get:

1 - 3x = x^2 + 6x + 9, or  x^2 + 6x + 8 + 3x, or

x^2 + 9x + 8 = 0.  Factoring, we get:  (x + 8)(x + 1) = 0, so that the solutions are {-1, -8}.

Answer:

I hope the given equation is :

{-1, -8}

First step to solve this equation to remove square root from the left side. So, take square on each sides of the equation. Therefore,

1 - 3x = (x + 3)²

1 - 3x = (x + 3)*(x + 3) Since a² = a * a

1 - 3x = x² + 3x + 3x + 3² By multiplication.

1 - 3x = x² + 6x + 9 Combine the like terms.

x² + 6x + 9 - 1 + 3x = 0 Subtract 1 and add 3x from each sides of equation

x² + 9x + 8 = 0 Combine the like terms.

Next step is to factor the trinomial to solve the above equation for x.

For that break downn the constant 8 into two multiples so that the addition of the multiples will result the coefficient of x = 9.

So, 8 = 1 * 8

Addition of 1 and 8 will give 9. So, next step is to replace 9x with 1x + 8x. So,

x² + 1x + 8x + 8 = 0

(x² + 1x) + (8x + 8) = 0 Group the terms.

x ( x + 1) + 8 (x + 1 ) = 0 Take out the common factor from each group.

(x +1 ) ( x + 8 ) = 0 Take out the common factor (x + 1).

So, x + 1 = 0 and x + 8 = 0 Set up each factor equal to 0.

Hence, x = -1 and - 8.

Next step is to plug in -1 and -8 in the original equation to cross check the solutions.

For x = -1,

Simplify each sides separately.

2 = 2

2 = 2 is correct. So, x = -1 satisfy the equation.

Hence, x = -1 is the real solution of the given equation.

Similarly let's plug in x = -8 now. So,

Simplify each sides separately.

5 = 2

5 = 2 is not true. So, x = -8 is the extraneous solution.

Therefore, the only solution is x = -1.

Hence, the correct choice is C.

Hope this helps you!

Step-by-step explanation:

mark brainlies plssssssssss

Answer: -1

Step-by-step explanation:

to calculate f(-1), you know that x = -1. so all you have to do is substitute:

f(-1) = (-1)2 + 1

f(-1) = -2 + 1

f(-1) = -1

Answer:

0

Step-by-step explanation:

Answer:

A,D and E

Step-by-step explanation:

We are given that a function

[tex]f(x)=49(\frac{1}{7})^x[/tex]

The given function is exponential function .

The exponential function is defined for all real values of x.

Therefore, domain of f=Set of  all real numbers

Substitute x=0

[tex]y=f(0)=49>0[/tex]

Range of f is greater than 0.

x=1

[tex]y(1)=\frac{49}{7}[/tex]

x=2

[tex]y=49(\frac{1}{7})^2=\frac{1}{7}y(1)[/tex]

As x increases by 1, each value of y is one-seventh of the previous y-value.

Therefore, option A,D and E are true.

Answer:

A D E

Step-by-step explanation:

Edge2020 quiz

Answer:

no

Step-by-step explanation:

No, it is not a random sample of the students in school.

Answer:

No

Step-by-step explanation:

A random sample is a sample that is taken from a larger set. Molly specifically chose to interview the youngest students, so the sample is not random.

Answer:

[tex]t=\frac{2567-2564}{\frac{11}{\sqrt{21}}}=1.250[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=21-1=20[/tex]  

the p value for this case would be given by:

[tex]p_v =2*P(t_{(20)}>1.250)=0.2113[/tex]  

For this case we see that the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2564 mm

Step-by-step explanation:

Information given

[tex]\bar X=2567[/tex] represent the mean height for the sample  

[tex]s=\sqrt{121}= 11[/tex] represent the sample standard deviation

[tex]n=21[/tex] sample size  

[tex]\mu_o =2564[/tex] represent the value that we want to test

[tex]\alpha=0.1[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to check if the true mean is equal to 2564 mm, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 2564[/tex]  

Alternative hypothesis:[tex]\mu \neq 2564[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing we got:

[tex]t=\frac{2567-2564}{\frac{11}{\sqrt{21}}}=1.250[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=21-1=20[/tex]  

the p value for this case would be given by:

[tex]p_v =2*P(t_{(20)}>1.250)=0.2113[/tex]  

For this case we see that the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2564 mm

Answer:

7 and 12

Step-by-step explanation:

7 and 12 are ok

17 is not

hope this helps

The solution of the inequality x < 17 will be all the real numbers less than 17. Then the correct options are A and B.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The inequality is given below.

x < 17

The solution of the inequality x < 17 will be all the real numbers less than 17. Then the correct options are A and B.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ2

Answer:

See Below

Step-by-step explanation:

x(2x) - 4(2x) + x(3) - 4(3)

= 2x² - 8x + 3x -12

= 2x²-5x-12

Answer:

The population proportion is 0.1057.

For samples of size n: Mean = 0.1057, Standard deviation [tex]s = \frac{0.3075}{\sqrt{n}}[/tex]

Step-by-step explanation:

Central Limit Theorem for Proportions:

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Population proportion:

Of 30,000 people, 3,170 people either drive a hybrid car or have indicated on a recent survey that they would be interested in driving one.

This means that [tex]p = \frac{3170}{30000} = 0.1057[/tex]

The population proportion is 0.1057.

Mean and standard deviation of the sampling distribution for samples of size n

By the Central Limit Theorem, the mean is [tex]\mu = p = 0.1057[/tex]

Standard deviation:

[tex]s = \sqrt{\frac{0.1057*0.8943}{n}} = \frac{0.3075}{\sqrt{n}}[/tex]

Work Shown:

log(200) = log(2^3*5^2)

log(200) = log(2^3) + log(5^2)

log(200) = 3*log(2) + 2*log(5)

log(200) = 3*q + 2*p

log(200) = 2p + 3q

The log rules I used were

log(A*B) = log(A)+log(B)

log(A^B) = B*log(A)

The equivalent expression of log(200) is 2p + 3q

The logarithmic expression is given as:

[tex]\mathbf{log 200}[/tex]

Rewrite as:

[tex]\mathbf{log(200) = log (25 \times 8)}[/tex]

Express as exponents

[tex]\mathbf{log(200) = log (5^2 \times 2^3)}[/tex]

Split

[tex]\mathbf{log(200) = log (5^2) +log(2^3)}[/tex]

Apply law of logarithms

[tex]\mathbf{log(200) = 2log (5) +3log(2)}[/tex]

From the question;

log(5) = p and log(2) = q

So, we have:

[tex]\mathbf{log(200) = 2p +3q}[/tex]

Hence, the equivalent expression of log(200) is 2p + 3q

Read more about logarithmic expressions at:

https://brainly.com/question/9665281

Answer:

[tex]x=2$\pm$\sqrt{42}[/tex]

Step-by-step explanation:

The given equation is:

[tex]x^{2} -4x-9=29\\\Rightarrow x^{2} -4x-9-29=0\\\Rightarrow x^{2} -4x-38=0[/tex]

Formula:

A quadratic equation [tex]ax^{2} +bx+c=0[/tex] has the following roots:

[tex]x=\dfrac{-b+\sqrt D}{2a}\ and\\x=\dfrac{-b-\sqrt D}{2a}[/tex]

Where [tex]D= b^{2} -4ac[/tex]

Comparing the equation with [tex]ax^{2} +bx+c=0[/tex]

a = 1

b = -4

c= -38

Calculating D,

[tex]D= (-4)^{2} -4(1)(-38)\\\Rightarrow D = 16+152 = 168[/tex]

Now, finding the roots:

[tex]x=\dfrac{-(-4)+\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4+2\sqrt {42}}{2}\\\Rightarrow x=2+\sqrt {42}\\and\\x=\dfrac{-(-4)-\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4-2\sqrt {42}}{2}\\\Rightarrow x=2-\sqrt {42}[/tex]

So, the solution is:

[tex]x=2$\pm$\sqrt{42}[/tex]

Answer is A or the first one

Answer:

7

Step-by-step explanation:

hh

ht

th

tt

so it's a 1/4 chance

1/4 * 28 = 7

Answer:

7

Step-by-step explanation:

The probability of both coins landing on heads is:

1/2 × 1/2 = 1/4

Multiply by 28.

1/4 × 28

= 7

Answer:

d) E = 8h + 0.05s

Her total sales in computers for the week is $2800.

Step-by-step explanation:

Let Rhea's hourly pay =h

She makes $8/hour, therefore sales for h hours =$8h

Let the volume of sales = s

She also earns 5% commission on sales = 5% of s = 0.05s

Therefore, the expression which best describes Rhea's total earnings:

(D) E=8h+0.05s

Rhea worked 15 hours last week and made $260 in total.

h=$15

From the formula

260=8(15)+0.05s

0.05s=260-8(15)

0.05s=140

s=2800

Her total sales in computers for the week is $2800.

Employers offer commissions to their employees to motivate them to seek to make sales rather than just passing time.

In so far as the sales commission do not eat up the profit of the business,  there are no potential problems with this form of earnings  

Answer:

13-n=4

Subtract both sides by 13

-n=-9

n=9

Step-by-step explanation:

13 less means - and a number means n that you don’t know. is means = sign. And so we get the answer that I gave you. Thank you

Answer:

$23161.10

Step-by-step explanation:

Assuming this is compounded annually, we use our simple interest rate formula: A = P(1 + r)^t

Step 1: Convert months to years

60 months/12 month/year = 5 years

Step 2: Plug in known variables

A = 18400(1 + 0.0471)^5

Step 3: Solve

When you plug step 2 into your calc you should get 23161.1 as your answer. I am assuming that this isn't compounded quarterly or monthly, but just yearly.

Answer:

26 can be divides evenly into 78 and 104 without leaving a remainder

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

78= 2 × 3 × 13

104= 2 × 2 × 2 × 13

The required number is: 2 × 13= 26

Answer:

7.5* 10^8

Step-by-step explanation:

(1.5 x 10^5)(5 x 10^3)

Multiply the numbers

1.5*5=7.5

Add the exponents

10 ^(5+3) = 10^8

Put back together

7.5* 10^8

This is in scientific notation

Answer:  55.6 days

Step-by-step explanation:

[tex]P=P_oe^{kt}\\\\\bullet \quad P=\dfrac{1}{2}P_0\\\bullet \quad k=-0.1247\\\bullet \quad t = unknown\\\\\\\dfrac{1}{2}P_o=P_oe^{-0.1247t}\\\\\\\dfrac{1}{2}=e^{-0.1247t}\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=-0.1247t\\\\\\\dfrac{ln\dfrac{1}{2}}{-0.1247}= t\\\\\\\large\boxed{55.6=t}[/tex]

Answer:

  Annuity C:  Deposit $72,000 one lump sum

Step-by-step explanation:

The yield is improved when the money is on deposit for a longer period.

If the $2400 annual deposit is made at the first of the year, then it will yield more than $600 deposits made at the first of each quarter.

If the $72,000 deposit is made at the beginning of the period, the entire amount is earning interest for the entire period.

  Annuity C will provide the largest yield.

Missing details to question is attached

Answer:

c) [tex] \frac{1}{4} [/tex]

Step-by-step explanation:

S

Required:

Find the probability that the account has a balance at least $500, given that it is at least 3 years old.

Which means: P(≥$500 | ≥3 years)

To find the probability, use the formula below:

P(≥$500 | ≥3 years) = (No. of accounts with balance≥ 500 and age ≥3 years) / (No. of accounts with age≥3 years)

Where from th given information:

Number of accounts with balance≥ 500 and age ≥3 years = 200

Number of accounts with age≥3 years = 600 + 200 = 800

Therefore,

P(≥$500 | ≥3 years) [tex] = \frac{200}{800} = \frac{1}{4} [/tex]

The probability that the account has a balance at least $500, given that it is at least 3 years old = [tex] \frac{1}{4} [/tex]

Answer:

each bag of candy is $6.00

Step-by-step explanation:

1 bag would cost $6.00

1×$6.00=$6.00

6 bags × $6.00 = $36.00

Answer:

the constant of proportionally is 6

the prices of 6 bags of candy is 36

Step-by-step explanation:

to find the constant u divide 6 by 1 to find how they multiplying it by

the prices for six bags is 36 bc u can do 6 times 6 or look at the graph and see that it lands on 36

hope this helps

Answer:

BRIAN DID NOT REACH HIS GOAL! Brian rode 5.52 miles!

Step-by-step explanation:

Answer:

he didn't reach his goal. he rode 5.52 miles

Step-by-step explanation:

Answer:  5,499,187,200

Step-by-step explanation:

A coin is tossed 5 times.  

There are two options (heads or tails) so the possible outcomes are: 2⁵

A six-sided die is rolled 4 times.

There are six options so the possible outcomes are: 6⁴

A group of 3 cards are drawn (without replacement).

The first outcome has 52 options, the second has 51 options, and the third has 50 options: 52 x 51 x 50

Now if we want the coin AND the die AND the cards, we have to multiply all of their possible outcomes:

     2⁵ x   6⁴  x  52 x 51 x 50

=   32 x 1296 x 132,600

=  5,499,187,200

Answer:

[tex]t=\frac{595-600}{\frac{20}{\sqrt{65}}}=-2.016[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=65-1=64[/tex]  

The p value would be given by:

[tex]p_v =2*P(t_{(64)}<-2.016)=0.048[/tex]  

And for this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mena is different from 600 mg

Step-by-step explanation:

Information given

[tex]\bar X=595[/tex] represent the sample mean

[tex]s=20[/tex] represent the sample standard deviation

[tex]n=65[/tex] sample size  

[tex]\mu_o =600[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test if the true mean is different from 600 mg, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 600[/tex]  

Alternative hypothesis:[tex]\mu \neq 600[/tex]  

The statistic would be given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info we got:

[tex]t=\frac{595-600}{\frac{20}{\sqrt{65}}}=-2.016[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=65-1=64[/tex]  

The p value would be given by:

[tex]p_v =2*P(t_{(64)}<-2.016)=0.048[/tex]  

And for this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mena is different from 600 mg

Answer:

x≤3

Step-by-step explanation:

9-3x≥2(x-3)

9-3x≥2x-6

-3x-2x≥-6-9

-5x≥-15

-5x/-5≥-15/-5

x≤3

Answer:

Step-by-step explanation:

The question is in complete. Here is the complete question.

"The dimensions of a triangular pyramid are shown below. The height of

the pyramid is 6 inches. What is the volume in cubic inches?

Base of triangle = 1in

height of triangle = 5in"

Given the dimension of the triangular base of base 1 inch and height 5inches with the height of the pyramid to be 6inches, the volume of the triangular pyramid is expressed as [tex]V = \frac{1}{3}BH[/tex] where;\

B = Base area

H = Height of the pyramid

Base area  B = area of the triangular base = [tex]\frac{1}{2}bh[/tex]

b = base of the triangle

h = height of the triangle

B = [tex]\frac{1}{2} * 5 * 1\\[/tex]

[tex]B = 2.5in^{2}[/tex]

Since H = 6inches

Volume of the triangular pyramid = [tex]\frac{1}{3} * 2.5 * 6\\[/tex]

[tex]V = 2.5*2\\V =5in^{3}[/tex]