Write and equation of the translated or rotated graph in general form (picture below)

Answer:

B, 3x - 5

Step-by-step explanation:

Factor by grouping to get (3x - 5)(2x + 3).

Factor 6x2−x−15

6x2−x−15

=(3x−5)(2x+3)

Answer:

(3x−5)(2x+3)

Answer:

48

Step-by-step explanation:

There are 3 events that are taking place.

Rolling a die which has 6 possible outcomes.

Flipping a coin which has 2 possible outcomes.

Spinning a spinner which has 4 possible outcomes.

Since the outcome of each event is independent of the other, the total possible outcomes will be equal to the product of outcomes of each event.

i.e.

Total outcomes = 6 x 2 x 4 = 48

The sample space of the experiment contains all the possible outcomes. so the number of elements in the sample space of this experiment will be 48

Answer:

The correct answer option is 48.

Step-by-step explanation:

Here in this experiment, three events are taking place that include rolling a die, flipping a coin and spinning a spinner.

The possible outcomes of each of these events are:

Rolling a die - 6

Flipping a coin - 2

Spinning a spinner - 4

Therefore, we can find the number of elements in the sample space of this environment by multiplying their possible outcomes.

Number of elements = 6 × 2 × 4 = 48

Answer:

0

Step-by-step explanation:

The given limit is

[tex]\lim_{x \to \infty} \frac{x^2+x-22}{4x^3- 13}[/tex]

Divide both the numerator and the denominator by the highest power of x in the denominator.

[tex]=\lim_{x \to \infty} \frac{\frac{x^2}{x^3}+\frac{x}{x^3}-\frac{22}{x^3}}{\frac{4x^3}{x^3}- \frac{13}{x^3}}[/tex]

This simplifies to;

[tex]=\lim_{x \to \infty} \frac{\frac{1}{x}+\frac{1}{x^2}-\frac{22}{x^3}}{4- \frac{13}{x^3}}[/tex]

As [tex]x\to \infty, \frac{c}{x^n} \to 0[/tex]

[tex]=\lim_{x \to \infty} \frac{0+0-0}{4- 0}=0[/tex]

The limit is zero

Answer:

Part a) The volume of the prism Q is two times the volume of the prism P

Part b) The volume of the prism Q is two times the volume of the prism P

Step-by-step explanation:

Part 18) we know that

The volume of a rectangular prism is equal to

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the prism

a) Suppose the bases of the prisms have the same area, but the height of prism Q is twice the height of prism P. How do the volumes compare?

Volume of prism Q

[tex]VQ=B(2h)=2(Bh)[/tex]

Volume of prism P

[tex]VP=Bh[/tex]

Compare

[tex]VQ=2VP[/tex]

so

The volume of the prism Q is two times the volume of the prism P

b) Suppose the area of the base of prism Q is twice the area of the base of prism P. How do the volumes compare?

Volume of prism Q

[tex]VQ=(2B)h=2(Bh)[/tex]

Volume of prism P

[tex]VP=Bh[/tex]

Compare

[tex]VQ=2VP[/tex]

The volume of the prism Q is two times the volume of the prism P

➷ The perimeter is the total of all the lengths / widths

The lengths can be represented by 4x - 7

The width can be represented by x

2 times the length + 2 times the width would equal the perimeter

2(x) + 2(4x - 7) = 136

Simplify:

2x + 8x - 14 = 136

10x - 14 = 136

Add 14 to both sides:

10x = 150

Divide both sides by 10:

x = 15

The width is equal to 15m

The length is 4(15) - 7 = 53m

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

49 units

Step-by-step explanation:

10.50u ≥ 200 + 6.40u       solve for u....

4.10u ≥ 200        (subtract 6.40u to both sides)

       u ≥ 200/4.10  (divide both sides by 4.10)

         u ≥ 48.78

         Any number of units greater than 48.78, but they can't sell parts of a unit, so 49 is the minimum number of units that need to be sold to make a profit  

Answer:

b. [tex]x=\frac{5\pi}{6}[/tex]

Step-by-step explanation:

The given function is

[tex]\sec x=-\frac{2\sqrt{3} }{3},\:\:for\:\:\frac{\pi}{2}\le x \le \pi[/tex]

Recall that the reciprocal of the cosine ratio is the secant ratio.

This implies that;

[tex]\frac{1}{\cos x}=-\frac{2\sqrt{3} }{3}[/tex]

[tex]\Rightarrow \cos x=-\frac{3}{2\sqrt{3} }[/tex]

[tex]\Rightarrow \cos x=-\frac{\sqrt{3}}{2}[/tex]

We take the inverse cosine of both sides to obtain;

[tex]x=\cos^{-1}(-\frac{\sqrt{3}}{2})[/tex]

[tex]x=\frac{5\pi}{6}[/tex]

Final answer:

Each person will get 1 cookie and there will be 3 cookies leftover.

Explanation:

In this scenario, we have 7 cookies that are being shared equally among 4 people. To find out how many cookies each person will get, we divide the total number of cookies by the number of people.

So, 7 cookies divided by 4 people = 1.75 cookies per person.

Since we can't divide a cookie into fractions, each person will get 1 cookie and there will be 3 cookies leftover.

➷ We'll work from here:

9x = 180

To isolate x, you would need to divide both sides by 9

x = 180/9

Solve:

x = 20

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer: ❤️Hello!❤️ x = 20

Step-by-step explanation:  Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :  

2*x+3*x+4*x-(180)=0  

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  9x - 180  =   9 • (x - 20)  

Step  2  :

Equations which are never true :

2.1      Solve :    9   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

2.2      Solve  :    x-20 = 0  

Add  20  to both sides of the equation :  

                     x = 20  

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=7850 \end{cases}\implies 7850=2\pi r\implies \cfrac{7850}{2\pi }=r\implies 1249.37\approx r[/tex]

Answer:

1249.37 units

Step-by-step explanation:

Answer:

d.   a_n = 6n - 4.

Step-by-step explanation:

The common difference (d)  is 8-2 = 14-8 = 20-14 = 26-20 = 6.

This is an Arithmetic Sequence with the first term (a1) is 2.

The general form of the explicit formula is a_n = a1 + d(n - 1)  so this sequence has  the formula:

a_n = 2 + 6(n - 1)

a_n = 2 + 6n - 6

a_n = 6n - 4.

The sequence is an illustration of an arithmetic sequence.

The explicit formula is: (d) [tex]a_n = 6n - 4[/tex]

We have:

[tex]a_1 = 2[/tex] -- the first term

Next, we calculate the common difference (d)

[tex]d = a_2 - a_1[/tex]

So, we have:

[tex]d = 8 -2[/tex]

[tex]d = 6[/tex]

The explicit formula is calculated using:

[tex]a_n = a_1 + (n - 1)d[/tex]

So, we have:

[tex]a_n =2 + (n - 1) \times 6[/tex]

Open bracket

[tex]a_n = 2 + 6n - 6[/tex]

Collect like terms

[tex]a_n = 6n - 6 + 2[/tex]

[tex]a_n = 6n - 4[/tex]

Hence, the explicit formula is: (d) [tex]a_n = 6n - 4[/tex]

Read more about arithmetic sequence at:

https://brainly.com/question/18109692

Answer:

a. [tex]\left[\begin{array}{cccc}9&-4&-5&|9\\7&4&-4&|-1\\6&-6&1&|-5\end{array}\right][/tex]

Step-by-step explanation:

The given system of equation is

[tex]9x-4y-5z=9[/tex]

[tex]7x+4y-4z=-1[/tex]

[tex]6x-6y+z=-5[/tex]

The coefficient matrix is :

[tex]\left[\begin{array}{ccc}9&-4&-5\\7&4&-4\\6&-6&1\end{array}\right][/tex]

The constant matrix is

[tex]\left[\begin{array}{c}9\\-1\\-5\end{array}\right][/tex]

The augmented matrix is obtained by  combining the coefficient matrix and the constant matrix.

[tex]\left[\begin{array}{cccc}9&-4&-5&|9\\7&4&-4&|-1\\6&-6&1&|-5\end{array}\right][/tex]

The correct choice is A

Answer:

Step-by-step explanation:

The formula of a volume of a rectangle prism:

[tex]V=lwh[/tex]

l - length

w - width

h - height

We have V = 72 cm³, w = 2 cm and h = 4 cm. Substitute:

[tex](2)(4)l=72[/tex]

[tex]8l=72[/tex]          divide both sides by 8

[tex]l=9\ cm[/tex]

Answer:

Option C [tex]9\ sandwiches[/tex]

Step-by-step explanation:

we know that

using proportion

[tex]\frac{1}{(1/3)}\frac{sandwich}{pounds}=\frac{x}{3}\frac{sandwiches}{pounds}\\ \\x=3*3\\ \\x=9\ sandwiches[/tex]

Answer:

9

Step-by-step explanation:

I got the answer from USATestprep

Answer:

a) 7069.82 Liters

b) 600 seconds

c) Shown below

d) (i) 0.6935 liters   (ii)  Since 0.6935 liters in 0.001 minute, so 693.5 liters per minute is as estimate (in liters per minute)

Step-by-step explanation:

a)

We simply put 5 into t of the equation and get the value of V. So:

[tex]V=10,000(0.933)^t\\V=10,000(0.933)^5\\V=7069.82[/tex]

So after 5 minutes the amount remaining is 7069.82 Liters

b)

half of the initial amount is half of 10,000 which is 5000. So we substitute 5000 into V and solve for t using logarithms.

Note: [tex]ln(a^b)=blna[/tex]

Thus, we have:

[tex]V=10,000(0.933)^t\\5000=10,000(0.933)^t\\0.5=(0.933)^t\\ln(0.5)=ln((0.933)^t)\\ln(0.5)=tln(0.933)\\t=\frac{ln(0.5)}{ln(0.933)}\\t=9.99[/tex]

Thus, t = 9.9949 minutes.

To get answer in seconds, we multiply by 60. Thus 9.9949*60= 600 seconds

c)

95% empty means 5% remaining. 5% of 10,000 = 0.05 * 10,000 = 500. We plug in 500 into V and solve for t as the previous step. Shown below:

[tex]V=10,000(0.933)^t\\500=10,000(0.933)^t\\0.05=0.933^t\\ln(0.05)=ln(0.933^t)\\ln(0.05)=tln(0.933)\\t=\frac{ln(0.05)}{ln(0.933)}\\t=43.1972[/tex]

So it takes around 43.1972 minutes to empty 95%. Since three-quarters of an hour is  [tex](\frac{3}{4})(60)=45[/tex] minutes, we have shown that the time it takes (43.1972 minutes) is very close to three-quarters of an hour.

d)

We plug in 0.001 into t and find V. Then we subtract that value from 10,000. This is just finding how much water has been removed in 0.001 minutes. Let's do this:

[tex]V=10,000(0.933)^t\\V=10,000(0.933)^{0.001}\\V=9999.3065\\Now\\10,000 - 9999.3065 = 0.6935[/tex]

So, 0.6935 liters

Answer: option b.

Step-by-step explanation:

To solve the given exercise, you must keep on mind the following law of logaritms:

[tex]m*log(a)=log(a)^m[/tex]

Descompose 8 into its prime factors:

[tex]8=2*2*2=2^3[/tex]

Therefore,  you can rewrite the expression given, as following:

[tex]log8=log2^3=3log2[/tex]

You know that [tex]log2=0.3010[/tex]

Then, when you substitute, you obtain:

[tex]3*0.3010[/tex]≈0.9030

Factor out 8 using 2.

log(8) = log(2^3)

Use the product rule [ log(xy) = log(x) + log(y) ] to simplify.

log(2^3) = 3 log(2)

Simplify using the given value for 2.

3(0.3010)

0.9030

Therefore, log(8) ≈ 0.9030 (Option B)

Best of Luck!

Answer:

p = 4

j = 21

Step-by-step explanation:

Joey = j

Pat = p

j = p + 17

(j+6) = 2*(p + 6) + 7      Simplify this. Remove the brackets.

j + 6 = 2p + 12 + 7        combine like terms    

j + 6 = 2p + 19               Subtract 6 from both sides

j +6-6 = 2p +19-6

j = 2p + 13

================

Equation j = 2p + 13 and j = p + 17

2p + 13 = p + 17                 Subtract p from both sides

2p-p+13 =p-p + 17

p + 13 = 17                         Subtract 13 from both sides

p = 17-13

p = 4

============

j = p + 17

j = 4 + 17

j = 21

Answer:

Joey is 21; Pat is 4

Step-by-step explanation:

The problem statement supports two equations in Joey's age (j) and Pat's age (p):

j - p = 17

(j +6) -2(p +6) = 7

Subtracting the second equation from the first, we have ...

(j -p) -((j +6) -2(p +6)) = (17) -(7)

p +6 = 10 . . . . . simplify

p = 4 . . . . . . . . . subtract 6

J = 17 +4 = 21

Joey is 21; Pat is 4.

Answer:

852

Step-by-step explanation:

Answer:

12+2 =14

Step-by-step explanation:

Answer: 1 and 13.

Step-by-step explanation: Because of the total, we know that the first number has to be less than 5, but greater than 0. to start in the median, let's use 3.

3+12 = 15.

That won't work, so let's try 2.

2+12 = 14.

There's the answer.

Answer:

460

Step-by-step explanation:

I=P x r x t

P is the principal amount, $2300.00.

r is the interest rate, 5% per year, or in decimal form, 5/100=0.05.

t is the time involved, 4....year(s) time periods.

So, t is 4....year time periods.

To find the simple interest, we multiply 2300 × 0.05 × 4 to get that:

The interest is: $460.00

Your room temperature is 25°C.

Step-by-step explanation:

hope this helps!

Probability of an event is the measure of its chance of occurrence.  The probability that the post box will outweigh the Kellogs box is 0.4129 approximately.

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z-score.

If we have

[tex]X \sim N(\mu, \sigma)[/tex]

(X is following normal distribution with mean [tex]\mu[/tex] standard deviation [tex]\sigma[/tex])

then it can be converted to standard normal distribution as

[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

[tex]P(Z \leq z) = P(Z < z) )[/tex]

Also, know that if we look for Z = z in z-tables, the p-value we get is

[tex]P(Z \leq z) = \rm p \: value[/tex]

Suppose that a random variable X is formed by [tex]n[/tex] mutually independent and normally distributed random variables such that:

[tex]X_i = N(\mu_i , \sigma^2_i) ; \: i = 1,2, \cdots, n[/tex]

And if

[tex]X = X_1 + X_2 + \cdots + X_n[/tex]

Then, its distribution is given as:

[tex]X \sim N(\mu_1 + \mu_2 + \cdots + \mu_n, \: \: \sigma^2_1 + \sigma^2_2 + \cdots + \sigma^2_n)[/tex]

If, for the given case, we assume two normally distributed random variables as:

X = variable assuming weights of boxes of Post Corn Flakes
Y = variable assuming weights of boxes of Kellogs

Then, as per the given data, we get:

[tex]X \sim N(\mu = 64.1, \sigma = 0.5)\\Y \sim N(\mu = 63.9, \sigma = 0.4)[/tex]

Then,  the probability that the Post box will outweigh the Kellogs box can be written as:

[tex]P(X > Y)[/tex]

Or,

[tex]P(X -Y > 0)[/tex]

We need to know about the properties of X-Y.

Also, since [tex]E(aX) = aE(X), Var(aX) = a^2Var(X)[/tex], thus,

[tex]-Y \sim N(-63.9, 0.4)[/tex]

As both are independent(assuming), thus,

[tex]X - Y \sim N(\mu = 64.1 - 63.9, \sigma = 0.5 + 0.4) = N(0.2, 0.9)[/tex]

Using the standard normal distribution, we get the needed probability as:

[tex]P(X -Y > 0) = 1 - P(X - Y \leq 0) \\P(X -Y > 0)= 1- P(Z = \dfrac{(X-Y) - \mu}{\sigma} \leq \dfrac{0 - 0.2}{0.9})\\P(X -Y > 0) \approx 1 - P(Z \leq -0.22)[/tex]

Using the z-tables, the p-value for Z = -0.22 is 0.4129

Thus, [tex]P(X > Y) = P(X - Y > 0) \approx 0.4129[/tex]

Thus, the probability that the post box will outweigh the Kellogs box is 0.4129 approximately.

Learn more about standard normal distribution here:

https://brainly.com/question/10984889

The probability that a randomly selected Post box outweighs a Kellogg's box is approximately 50%.

To find the probability that the Post box will outweigh the Kellogg's box, we need to calculate the difference in weights between the two brands and then determine the probability that this difference is positive.

Let X be the weight of a box of Post Corn Flakes and Y be the weight of a box of Kellogg's Corn Flakes.

We are given that:

- For Post Corn Flakes, X ~ N(μ = 64.1, σ = 0.5)

- For Kellogg's Corn Flakes, Y ~ N(μ = 63.9, σ = 0.4)

We want to find P(X > Y), which is the probability that a randomly selected box of Post Corn Flakes weighs more than a randomly selected box of Kellogg's Corn Flakes.

Now, let Z = X - Y. We are interested in finding P(Z > 0).

The mean and standard deviation of Z can be calculated as follows:

- Mean of Z: μ_Z = μ_X - μ_Y = 64.1 - 63.9 = 0.2 oz

- Standard deviation of Z: σ_Z =[tex]sqrt(σ_X^2 + σ_Y^2) = sqrt(0.5^2 + 0.4^2)= sqrt(0.25 + 0.16)= sqrt(0.41) = 0.64 oz[/tex]

Now, we standardize Z:

Z = (X - Y - μ_Z) / σ_Z

Therefore,

P(Z > 0) = P((X - Y - μ_Z) / σ_Z > 0)

         = P((X - Y) > μ_Z)

         = P((X - Y) > 0.2)

Now we look up the z-score corresponding to Z = 0.2:

z = (0.2 - μ_Z) / σ_Z

  = (0.2 - 0.2) / 0.64

  = 0

The probability that Z is greater than 0 is equal to the probability that the standardized Z-score is greater than 0, which is 0.5.

Therefore, the probability that the Post box will outweigh the Kellogg's box is 0.5 or 50%.

Answer:

[tex]x=-0.75[/tex]

Step-by-step explanation:

The given equation is

[tex]4^{-5x-7}=6^{2x-1}[/tex]

We take logarithm of both sides to base 10.

[tex]\log(4^{-5x-7})=\log(6^{2x-1})[/tex]

[tex](-5x-7)\log(4)=(2x-1)\log(6)[/tex]

We expand the brackets to get;

[tex]-5x\log(4)-7\log(4)=2x\log(6)-\log(6)[/tex]

Group similar terms;

[tex]-7\log(4)+\log(6)=2x\log(6)+5x\log(4)[/tex]

[tex]-7\log(4)+\log(6)=(2\log(6)+5\log(4))x[/tex]

[tex]\frac{-7\log(4)+\log(6)}{(2\log(6)+5\log(4))}=x[/tex]

[tex]x=-0.752478[/tex]

To the nearest hundredth.

[tex]x=-0.75[/tex]

Answer:

1 hour

Step-by-step explanation:

1/4 of 4 is 1

Answer:one hour

Step-by-step explanation:

The original width was 6 inches, the new width is 9 inches.

Divide the new width by the original width to find the scale factor:

9/6 = 1.5

Now multiply the original height by the scale factor to find the new height:

4 x 1.5 = 6 inches.

Answer:

  P = 10x³ + 4x² + 8x + 6

Step-by-step explanation:

The perimeter of a rectangle is twice the sum of length and width.

  P = 2(L+W) = 2((x³ +2x² -6x +12) +(4x³ +10x -9))

  = 2(5x³ +2x² +4x +3) . . . . collect terms inside parentheses

  P = 10x³ +4x² +8x +6

Answer:

Step-by-step explanation:

The formula of a volume of a cylinder:

[tex]V=\pi r^2H[/tex]

r - radius

H - height

We have r = 1cm and H = 21cm. Substitute:

[tex]V=\pi(1^2)(21)=21\pi\ cm^3[/tex]

The formula of a cone:

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

We have V = 21π cm³ and H = 7cm. Substitute:

[tex]\dfrac{1}{3}\pi(r^2)(7)=21\pi[/tex]        divide both sides by π

[tex]\dfrac{1}{3}(7)(r^2)=21[/tex]         divide both sides by 7

[tex]\dfrac{1}{3}r^2=3[/tex]         multiply both sides by 3

[tex]r^2=9\to r=\sqrt9\\\\r=3\ cm[/tex]

Answer:

A 3cm

Step-by-step explanation:

[tex]x - |-20| = |-34|\\x-20=34\\x=54[/tex]

Answer:

27

Step-by-step explanation:

We figure out the scale factor first, which is the number of times one radius is of the other.  We call the scale factor, k.

To get how many times larger is the volume of similar spheres, we will need to cube the scale factor.

Since it is given that radius of Sphere A is 3 times that of Sphere B, we can say that the scale factor (k) = 3. Hence, the volume of Sphere A would be k^3 times the volume of Sphere B.

So,  [tex]k^3\\=(3)^3\\=27[/tex]

Hence, the volume of sphere A is 27 times the volume of sphere B.