Which expression is equivalent to (5^-2) (5^-1)

-1/125
-1/5
1/125
1/5

Answer:

The y-intercept of the function [tex]f(x)=2x^{2}+x-4[/tex] is [tex](0,-4)[/tex]

Step-by-step explanation:

Therefore, we can write the y-intercept as :

[tex]y-intercept=(0,a)[/tex]

We obtain the another coordinate ''a'' replacing ''x'' by a ''0'' in the function.

In this exercise, the function is:

[tex]f(x)=2x^{2}+x-4[/tex]

If x = 0 ⇒

[tex]f(0)=2(0)^{2}+0-4=-4=a[/tex]

We find that ''-4'' is the coordinate ''a'' that we were looking for.

We conclude that the point [tex](0,a)=(0,-4)[/tex]

And [tex](0,-4)[/tex] is the y-intercept of the function.

the greatest rectangular area is actually a square

 so 376/4 = 94 feet.

 each side will be 94 feet

 area of a square is 94^2

= 94 * 94 = 8836 square feet

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

Initial wildflowers in the first year = 1200

Every year, the number of wildflower is one fourth of the previous year.

So, it form a geometric series:

1200,300,75............

so, using sigma notation we can express the infinite growth of the wildflowers:

[tex]\sum ^{\infty}_{i=1}1200(\dfrac{1}{4})^{i-1}[/tex]

As we know that sum of infinite terms in case of geometric series is given by

[tex]S_{\infty}=\dfrac{a}{1-r}\\\\S_{\infty}=\dfrac{1200}{1-0.25}\\\\S_{\infty}=\dfrac{1200}{0.75}\\\\S_{\infty}=1600[/tex]

Therefore, there are 1600 wildflowers.

Hence, Third option is correct.

In the given parallelogram ABCD, angle $a$ is 62 degrees and angle $adb$ is 75 degrees. Angle $bd$ is calculated to be 105 degrees making angle $adc$ the supplementary to $bd$, and therefore also 75 degrees.

In a parallelogram, opposite angles are equal and consecutive angles are supplementary (adding up to 180 degrees). In your given quadrilateral $abcd$, the measure of angle $a$ is 62 degrees and $a$ and $adb$ are consecutive angles. Therefore, knowing that angle $adb$ is 75 degrees, angle $bd$ should be the supplementary to $adb$, which is 180 - 75 = 105 degrees. Finally, since $adc$ is a straight line and $bd$ and $dc$ are parts of it, therefore angle $dc$ = 180 - angle $bd$ = 180 - 105 = 75 degrees. So, the measure of angle $adc$ is 75 degrees.

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You should first solve each equation for y.

Eliminate answer choices with wrong slopes or y intercepts.

Then, because it is a dotted line, the answer will only be < or >.

And because the area is shaded to the right, it would mean that x > y.

So the answer is A) 3x - y > 3

Answer:

The correct option is A.

Step-by-step explanation:

If a line passing through two points then the equation of line is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

From the given graph it is clear that the related line passing through the points (0,-3) and (1,0). So, the equation of related line is

[tex]y-(-3)=\frac{0-(-3)}{1-0}(x-0)[/tex]

[tex]y+3=3x[/tex]

The (0,0) is not in the solution set. So check the equation be (0,0).

[tex]0+3=3(0)[/tex]

[tex]3=0[/tex]

This condition is false if the sign of inequality is < or ≤. Since the related line is a solid line, therefore the sign of inequality must be <.

The required inequality is

[tex]y+3<3x[/tex]

[tex]3<3x-y[/tex]

It is also written as

[tex]3x-y>3[/tex]

Therefore the correct option is A.

3275 = x * (1+0.075/12)^(12*10)

3275 = x * (2.11206463)

x= 3275/2.11206463 = 1550.6154

x=1550.62

she needs to deposit $1,550.62

Answer:

I believe Homer "the genius" math to be incorrect for Part A. (-30)^2+60(30)-116= 900+1800-116=2584; not 784 as he got -900 when squaring -30.

Step-by-step explanation:

Answer:

The First person who answered it was wrong! Its 32,760 I took the test lol!

Step-by-step explanation:

 nPr = n!/(n-r)! <-- The equation used for this.

The probability of answering all the question correctly is [tex]\boxed{\bf \dfrac{1}{256}}[/tex]

Further Explanation:

Given:

The total number of question is [tex]4[/tex].

Each question has [tex]4[/tex] options and one is correct.

Concept used:

Probability is defined as the ratio of number of favorable outcomes to number of total outcomes.

[tex]\boxed{\text{Probability}=\dfrac{\text{favorable outcomes}}{\text{total outcomes}}}[/tex]

Calculation:

The probability of getting the correct answer is calculated as follows:

[tex]\begin{aligned}P&=\dfrac{1}{4}\\&=0.25\end{aligned}[/tex]

The probability of getting the incorrect answer is calculated as follows:

[tex]\begin{aligned}P&=1-\dfrac{1}{4}\\&=1-0.25\\&=0.75\end{aligned}[/tex]

The formula for probability of answering all question correctly is as follows:

[tex]\boxed{P'=^nC_{r}P^{r}(1-P)^{n-r}}[/tex]

Here, [tex]n[/tex] is number of question and [tex]r[/tex] is number of correct answer, [tex]P'[/tex] is the probability of answering all question correctly.

Solve the above equation to obtain probability of answer all question correctly.

Substitute [tex]4[/tex] for [tex]n[/tex], [tex]0.25[/tex] for [tex]P[/tex] and [tex]4[/tex] for [tex]r[/tex] in above equation to obtain probability of answering all question correctly.

[tex]\begin{aligned}P'&=^4C_{4}(0.25)^{4}(1-0.25)^{4-4}\\&=\dfrac{4!}{(4-4)!\cdot 4!}\left(\dfrac{25}{100}\right)^{4}(0.75)^{0}\\&=\left(\dfrac{1}{4}\right)^{4}\\&=\dfrac{1}{256}\end{aligned}[/tex]  

Therefore, the probability of the correct answer is [tex]0.25[/tex].

The probability of the incorrect answer is [tex]0.75[/tex].

The probability of answering all question correctly is [tex]\dfrac{1}{256}[/tex].

Thus, the probability of answering all question correctly is [tex]\boxed{\dfrac{1}{256}}[/tex].

Learn more:

1. Simplification: https://brainly.com/question/1602237

2. Quadratic equation: https://brainly.com/question/1332667

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Probability

Keywords: Probability, Question, Richard, multiple choice, four answer, class, attend, guesses, correctly answer, favorable outcomes, total outcomes.

The probability that Richard will answer all four questions correctly is 0.004.

The probability that Richard will answer all four questions correctly can be determined by multiplying the probability of getting one question correct by itself for each question. Since each question has four answer choices and only one is correct, the probability of guessing the correct answer for one question is 1/4.

Therefore, the probability of Richard answering all four questions correctly is (1/4) * (1/4) * (1/4) * (1/4) = 1/256. Rounded to three decimal places, this probability is approximately 0.004.

Thus, the probability that Richard will answer all questions correctly is 0.004.

Answer:

The equation which represents the statement thirteen less then a number is forty two is:

x-13=42

Step-by-step explanation:

Let x be any number

we are given that:

thirteen less then a number is forty two

i.e. x-13=42

Hence, the equation which represents the statement thirteen less then a number is forty two is:

x-13=42

Answer: h(x) = 3x(2 - 3x)

Step-by-step explanation:

Here the given functions are,

[tex]f(x) = x(2-x)[/tex]

[tex]g(x) = 3x[/tex]

[tex]h(x) = f(x) \circ g(x) = (f\circ g)(x) = f[g(x)][/tex]

[tex]= f( 3x )[/tex]

[tex]= (3x)[2-(3x)][/tex]

[tex]= 3x(2-3x)[/tex]

Hence,

[tex]h(x) = 3x(2-3x)[/tex]

⇒ Fourth option is correct.

Factoring this trinomial as the product of two binomials,

we have (x - 9)(x + 2) and set that equal to 0.

So we have (x - 9)(x + 2) = 0.

So either x - 9 = 0 or x + 2 = 0.

Solving for x in each equation, we find that our solution is {9, -2}.