A piece of buttered toast falls to the floor 17 times. The toast landed buttered side up 6 times. What is the probability that the toast lands buttered side down?

Answer:

x = - 4, x = 2

Step-by-step explanation:

Given

3x² + 6x - 24 = 0 ( divide through by 3 )

x² + 2x - 8 = 0 ← in standard form

(x + 4)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 2 = 0 ⇒ x = 2

Answer: negative 0.7

Step-by-step explanation:because you are looking for the opposite if you make a number line

Answer: r = 11

Step-by-step explanation:

We know that the point (-2, r) lies on the graph of:

2*x + y = 7.

Then, if we that point is on the graph of the equation, we can replace the values and we will have:

2*(-2) + r = 7

and now we solve this for r-

-4 + r = 7

r = 7 + 4 = 11

r = 11

Answer:

[tex]\boxed{x \leq -4}[/tex]

Step-by-step explanation:

Hey there!

Well to solve for x in,

16x - 7 ≤ -71

We need to single out x.

16x - 7 ≤ -71

+7 to both sides

16x ≤ -64

Divide both sides by 16

x ≤ -4

Hope this helps :)

Answer:

x ≤ -4

I hope this helps!

Answer:

Step-by-step explanation:

f(g(0))=

g(0)= 6(0) + 4 = 0 + 4 = 4

f(4)= 4(4)+5 = 16 + 5 = 21

g(f(0))=

f(0)= 4(0)+5 = 0+5 = 5

g(5)= 6(5)+4 = 30+4= 34

Answer:

c = 0.25m + 50

Step-by-step explanation:

Let c = cost; let m = number of minutes.

c = 0.25m + 50

Answer:

Step-by-step explanation:

Scholarship and grants are money given to the candidates to support his financial needs in school. It will serves as the means of revenue for the student.

Revenue generated = Grant + Scholarship amount

Revenue generated = $350 + $400

Revenue generated= $750

Total money needed to be spent in school = Tuition + fees

If tuition is $113.67 per credit hour and I used 15 credit hours, total amount of tuition paid = 15* $113.67 =  $1705.05

Total fees =  $660

Total money needed to be spent in school = $1705.05 + $660

Total money needed to be spent in school =  $2365.05

Amount I will need to pay for classes next semester = Total money that will be spent - (grant+scholarship)

=  $2365.05 - $750

= $1615.05

Hence, the amount I will need to pay for classes next semester is  $1615.05

Answer:

The area of the pyramid is 360 unit²

Step-by-step explanation:

Given

Base Edge, a = 10

Height, h = 12

Required

Determine the surface area

The surface area of a regular pyramid is calculated as thus;

[tex]A = a^2 + 2a\sqrt{\frac{a^2}{4} + h^2}[/tex]

Substitute values for a and h

[tex]A = 10^2 + 2 * 10 * \sqrt{\frac{10^2}{4} + 12^2}[/tex]

Evaluate all squares

[tex]A = 100 + 2 * 10 * \sqrt{\frac{100}{4} + 144}[/tex]

[tex]A = 100 + 2 * 10 * \sqrt{25 + 144}[/tex]

[tex]A = 100 + 2 * 10 * \sqrt{169}[/tex]

Take positive square root of 169

[tex]A = 100 + 2 * 10 * 13[/tex]

[tex]A = 100 + 260[/tex]

[tex]A = 360[/tex]

Hence, the area of the pyramid is 360 unit²

Answer:

B.) 360 units2

Step-by-step explanation:

I got it correct on founders education

Answer:

sine and tangent

will be positive.

Answer:

The P​-value is the probability of getting a test statistic at least as extreme as the one representing the sample​ data, assuming that the null hypothesis is true.

Step-by-step explanation:

The P​-value is the probability of getting a test statistic at least as extreme as the one representing the sample​ data, assuming that the null hypothesis is true.

The p-value is the probability that, if the null hypothesis were true,sampling variation would yield and estimate that is further away from the hypothesised value than our data estimate. The p-value shows us how possible it is to get a result like this if the null hypothesis is true.

Assuming we have a null hypothesis and an alternative hypothesis computed as follows.

[tex]H_o : \mu = 5 \\ \\ H_1 : \mu \neq 0.5[/tex]

If P-value is less than or equal to [tex]\mu[/tex] , we will reject the null hypothesis.

Answer:

7

Step-by-step explanation:

The following range includes numbers from negative infinity to 8. But, 8 isn't included, because there is a parentheses not a bracket. So, basically you can have 7.9999999. But, it asks for an integer, so it is 7.

The largest integer which belongs to the interval: (−∞, 8) is 7

To determine the largest integer, we will first ascertain what the use of parentheses and brackets denote.

The use of parentheses ( ) stands for open interval, that is, the extreme numbers of the set are not included.

If the brackets [ ] were used instead, that will be closed interval, that is, the extreme numbers of the set are included.

Since ( ) were used in the question, that means the extreme numbers −∞ and 8 are NOT included in the set.

Now, let us define an integer.

An integer is a positive or negative whole number or zero.

Hence, the integers in the set will include: −∞+1, −∞ + 2, ... 5, 6, and 7.

The largest integer here is 7

Hence, the largest integer which belongs to the interval: (−∞, 8) is 7

Learn more in the link below:

https://brainly.com/question/13324131

Answer:

d) F2 = -F1.

Step-by-step explanation:

According to Coulomb's law of forces on electrostatic charges, the force of attraction is proportional to the product of their charges, and inversely proportional to the square of their distance apart.

What this law means is that both particles will experience an equal amount of force on them, due to the presence of the other particle. This force is not just as a result of their individual charges, but as a result of the product of their charges. Also, the force is a vector quantity that must have a direction alongside its magnitude, and the force on the two particles will always act in opposite direction, be it repulsive or attractive.

Answer:

(MOE) the Margin of Error will decrease by the square root of 2

Step-by-step explanation:

The Margin of Error (MOE) is an inverse function of sample size n ( more precisely of the square root of sample size ). That relation means changes in sample size ( keeping constant other variables of the distribution) will imply opposite changes in the Margin of Error. If we double the sample size increasing it from 200 up to 400,  the Margin of Error will decrease by the square root of 2

Answer:

The answer is usted

Step-by-step explanation:

And if you want to learn more download duolingo

Answer:

Option C - Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.

Step-by-step explanation:

First of all let's define the hypothesis;

Null hypothesis;H0; μ = $48,722

Alternative hypothesis;Ha; μ > $48,722

Now, let's find the test statistic for the z-score. Formula is;

z = (x' - μ)/(σ/√n)

We are given;

x' = 48,722

μ = 49,870

σ = 3900

n = 50

Thus;

z = (49870- 48722)/(3900/√50)

z = 2.08

So from online p-value calculator as attached, using z = 2.08 and α = 0.05 ,we have p = 0.037526

This p-value of 0.037526 is less than the significance value of 0.05,thus, we reject the claim that that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722

Answer:

Step-by-step explanation:

Using FV = PV(1 + r)^n where FV = future value, PV = present value, r = interest rate per period, and n = # of periods

1/PV (FV) = (PV(1 + r^n)1/PV divide by PV

ln(FV/PV) = ln(1 + r^n) convert to natural log function

ln(FV/PV) = n[ln(1 + r)] by simplifying

n = ln(FV/PV) / ln(1 + r) solve for n

n = ln(2/1) / ln(1 + .08) solve for n, letting FV + 2, PV = 1 and rate = 8% or .08 compound annually

n = 9

n = ln(2/1) / ln(1 + .08/12) solve for n, letting FV + 2, PV = 1 and rate = .08/12 compound monthly

n = 104 months or 8.69 years

n = ln(2/1) / ln(1 + .08/365) solve for n, letting FV + 2, PV = 1 & rate = .08/365 compound daily

n = 3163 days or 8.67 years

Alternatively

A = P e ^(rt)

Given that r = 8%

= 8/100

= 0.08

2 = e^(0.08t)

ln(2)/0.08 = t

0.6931/0.08 = t

t= 8.664yrs

t = 8.67yrs

Which ever approach you choose to use,you will still arrive at the same answer.

Answer:

Questions .(1) 2/m. (2). m-1 . (3) 2 . (4) m

Answer:

2m(m-2)/2(m-2)= m

(m-1)(m-1)/m-1   ⇒ ( m-1/m-1)=1

Step-by-step explanation:

a.

[tex]s \: = \frac{k}{g} [/tex]

[tex]8 = \frac{k}{1.5} [/tex]

[tex]k \: = 1.5 \times 8 = 12[/tex]

[tex]s = \frac{12}{g} [/tex]

b.

[tex]s = \frac{12}{3} [/tex]

s = 4

Answer:

2  1/5

Step-by-step explanation:

2 3/4 * 4/5

Change the mixed number to an improper fraction

( 4*2+3)/4 * 4/5

11/4 * 4/5

The 4 in the numerator and denominator cancel

11/5

Changing back to a mixed number

5 goes into 11 2 times with 1 left over

2 1/5

Answer:

[tex]2\frac{1}{5}[/tex]

Step-by-step explanation:

[tex]2\frac{3}{4}*\frac{4}{5}\\\frac{11}{4}*\frac{4}{5}\\\frac{11}{5}\\ 2\frac{1}{5}[/tex]

Answer:

Step-by-step explanation:

Given the limit of the function [tex]\lim_{(x,y) \to (0,0)} \frac{x^4-34y^2}{x^2+17y^2}[/tex], to find the limit, the following steps must be taken.

Step 1: Substitute the limit at x = 0 and y = 0 into the function

[tex]= \lim_{(x,y) \to (0,0)} \frac{x^4-34y^2}{x^2+17y^2}\\= \frac{0^4-34(0)^2}{0^2+17(0)^2}\\= \frac{0}{0} (indeterminate)[/tex]

Step 2: Substitute y = mx int o the function and simplify

[tex]= \lim_{(x,mx) \to (0,0)} \frac{x^4-34(mx)^2}{x^2+17(mx)^2}\\\\= \lim_{(x,mx) \to (0,0)} \frac{x^4-34m^2x^2}{x^2+17m^2x^2}\\\\\\= \lim_{(x,mx) \to (0,0)} \frac{x^2(x^2-34m^2)}{x^2(1+17m^2)}\\\\\\= \lim_{(x,mx) \to (0,0)} \frac{x^2-34m^2}{1+17m^2}\\[/tex]

[tex]= \frac{0^2-34m^2}{1+17m^2}\\\\= \frac{34m^2}{1+17m^2}\\\\[/tex]

Since there are still variable 'm' in the resulting function, this shows that the limit of the function does not exist, Hence, the function DNE

Answer:

-9p -4q + 69

Step-by-step explanation:

5p +4q + (-9p +69)

=> 5p + 4q -9p +69

=> -4p +4q +69

Now, we need to subtract 5p +8q from -4p + 4q +69

=> -4p +4q +69 - (5p +8q)

=> -4p + 4q +69 - 5p -8q

=> -9p -4q + 69

Answer:

x=4

Step-by-step explanation:

To solve for x, we must get x by itself on one side of the equation.

[tex]\sqrt{x} +5-3=4[/tex]

First, we can combine like terms on the left side. Subtract 3 from 5.  

[tex]\sqrt{x} +(5-3)=4[/tex]

[tex]\sqrt{x} +2=4[/tex]

2 is being added on to the square root of x. The inverse of addition is subtraction. Subtract 2 from both sides of the equation.

[tex]\sqrt{x} +2-2=4-2[/tex]

[tex]\sqrt{x} = 4-2[/tex]

[tex]\sqrt{x} =2[/tex]

The square root of x is being taken. The inverse of a square root is a square. Square both sides of the equation.

[tex](\sqrt{x} )^{2} =2^2[/tex]

[tex]x=2^2[/tex]

Evaluate the exponent.

2^2= 2*2 =4

[tex]x=4[/tex]

Let's check our solution. Plug 4 in for x and solve.

[tex]\sqrt{x} +5-3=4[/tex]

[tex]\sqrt{4} +5-3=4[/tex]

[tex]2+5-3=4[/tex]

[tex]7-3=4[/tex]

[tex]4=4[/tex]

Our solution checks out, so we know x=4 is correct.

Answer:

k = 5

Step-by-step explanation:

I will assume that your polynomial is

x^2 - 3x^2 + kx + 14

If x - a is a factor of this polynomial, then a is a root.

Use synthetic division to divide (x - 2) into x^2 - 3x^2 + kx + 14:

 2      /      1     -3     k     14

                        2     -2    2k - 4

         -------------------------------------

               1        -1    (k - 2)   2k - 10

If 2 is a root (if x - 2 is a factor), then the remainder must be zero.

Setting 2k - 10 = to zero, we get k = 5.

The value of k is 5 and the polynomial is x^2 - 3x^2 + 5x + 14

Answer:

3sqrt(2)

Step-by-step explanation:

sqrt(32) - sqrt(2)

rewriting sqrt(32)

sqrt(16*2) - sqrt(2)

sqrt(16) * sqrt(2)  - sqrt(2)

4 sqrt(2) - sqrt(2)

3sqrt(2)

Answer:

Low             Q1                Median              Q3                 High

6                  9                     11                      12.5                14

The interquartile range = 3.5

Step-by-step explanation:

Given that:

Consider the following ordered data. 6 9 9 10 11 11 12 13 14

From the above dataset, the highest value = 14  and the lowest value = 6

The median is the middle number = 11

For Q1, i.e the median  of the lower half

we have the ordered data = 6, 9, 9, 10

here , we have to values as the middle number , n order to determine the median, the mean will be the mean average of the two middle numbers.

i.e

median = [tex]\dfrac{9+9}{2}[/tex]

median = [tex]\dfrac{18}{2}[/tex]

median = 9

Q3, i.e median of the upper half

we have the ordered data = 11 12 13 14

The same use case is applicable here.

Median = [tex]\dfrac{12+13}{2}[/tex]

Median = [tex]\dfrac{25}{2}[/tex]

Median = 12.5

Low             Q1                Median              Q3                 High

6                  9                     11                      12.5                14

The interquartile range = Q3 - Q1

The interquartile range =  12.5 - 9

The interquartile range = 3.5

Answer:  A)  g(x) = 3x - 14

Step-by-step explanation:

Solve the equation for y and replace y with g(x):

y - 3x = -14

y        = 3x - 14

  g(x) = 3x - 14

Answer:

infinite solutions

Step-by-step explanation:

x+6+8=2x-x+14

x+6+8=x+14

x+14=x+14

14=14

or

x=x

plug in any number

2+6+8=2(2)-2+14

16=16

another example

8+6+8=2(8)-8=14

22=22