A standard deck of cards contains 52 cards. One card is selected from the deck. ​(a) Compute the probability of randomly selecting a diamond or club. ​(b) Compute the probability of randomly selecting a diamond or club or heart. ​(c) Compute the probability of randomly selecting a three or club.

Answer:

[tex]\boxed{\sf \ \ \ k = 1 \ \ \ }[/tex]

Step-by-step explanation:

hello,

saying that p-1 is a factor of [tex]p^4+p^2-p-k[/tex]

means that 1 is a root of this expression, so it comes

1+1-1-k=0

<=> 1-k=0

<=> k = 1

Answer:

Option (2)

Step-by-step explanation:

The given table represents the relation between the velocity and the time for an object is falling under the gravity.

Change in velocity with respect to time is directly proportional so the change is linear.

Acceleration due to gravity of this object is defined by the slope of the line joining the ordered pairs given in the table.

Let the two points lying on the line are (0, 0) and (1, 9.8)

Slope of the line passing through two points = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]

                                                                          = [tex]\frac{9.8-0}{1-0}[/tex]

                                                                          = 9.8 [tex]\frac{m}{s^{2} }[/tex]

Option (2) will be the answer.

Answer:

3 miles per hour

Step-by-step explanation:

Jessica is walking home from a friend's house.

After 2 minutes she is 0.8 miles from the home and after 12 minutes she is 0.3 miles away fro her house.

Her rate will be = (change in distance)/change in time

= (0.8-0.3)/(12-2)

= 0.5/10

= 0.05 miles per minute

Now we will convert timings from minutes to hour.

Or  = 0.05×60  

= 3 miles per hour

Answer: 2x²-√3

Step-by-step explanation:

Another way to say the conjugate is the opposite. All you have to do is to change the sign in the binomial, which is 2x²+√3. When you change the sign, it becomes 2x²-√3.

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:

  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.

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: -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:

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:

[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:  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:

4y = -3x +18

Step-by-step explanation:

Let's get the gradient from this line equation first.

4x-3y=10

4x-10=3y

Y= 4/3x -10/3

The gradient is 4/3.

For a line perpendicular to another line.

M*M'= -1

M= -/(4/3)

M = -3/4

So the gradient to be used is -3/4

Formula for solving is

(Y-y1)/(x-x1)= M

X1= 2

Y1= 3

M = -3/4

(Y-y1)/(x-x1)= M

(Y-3)/(x-2)= -3/4

4(y-3)= -3(x-2)

4y -12 = -3x +6

4y = -3x +18

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:  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 :

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:

See Below

Step-by-step explanation:

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

= 2x² - 8x + 3x -12

= 2x²-5x-12

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:

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:

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

value of x is 34 degrees  

Step-by-step explanation:

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

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:

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]

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:

Step-by-step explanation:

A parallelogram is a quadrilateral with congruent opposite sides and pair of opposite angles.

Given: parallelogram ABCD

          AD≅ BC

          AD ║ BC

Thus;

<ABC + DAB = [tex]180^{o}[/tex] (supplementary angle property)

ΔABD = ΔCBD (each diagonal divides a parallelogram into two congruent triangles)

<ABC = <ADC (both pairs of opposite angles are congruent)

<DAB = <BCD (both pairs of opposite angles are congruent)

AB ≅ CD (opposite sides are congruent)

AB ║ DC (pair of opposite sides are parallel)

Therefore, the quadrilateral ABCD is a parallelogram.

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:

Cash, Bonds, Stocks and Mutual funds

Step-by-step explanation:

The four major categories of securities are:  

These 4  major categories are evaluated as given below: