Find the value of each variable.

A. a = 15, b = 5, c = 8, d = 4

B. a = 15, b = 4, c = 8, d = 5

C. a = 14.5, b = 5, c = 6, d = 4

D. a = 14.5, b = 4, c = 6, d = 5

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].

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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:

34.77

Step-by-step explanation:

The area of a triangle with sides of length 6 cm, 4 cm, and 7 cm is approximately 11.95 cm² when calculated using Heron's formula and rounded to two decimal places.

The original question appears to be incomplete as there's no clear indication of which measure is being sought for the triangle with sides of length 6 cm, 4 cm, and 7 cm. However, if the goal is to use these sides to determine the area of a triangle, we can use Heron's formula, since the lengths given do not form a right triangle.

First, calculate the semiperimeter (s):

(s) = (a + b + c) / 2

(s) = (6 + 4 + 7) / 2

(s) = 17 / 2

(s) = 8.5 cm

Now, apply Heron's formula which is Area [tex](A) = \sqrt{[ (s)((s)-a)((s)-b)((s)-c) ][/tex]:

[tex]A = \sqrt{[8.5(8.5-6)(8.5-4)(8.5-7)]}\\A = \sqrt{[8.5(2.5)(4.5)(1.5)]}\\A = \sqrt{[8.5 \times 2.5 \times 4.5 \times 1.5]}\\A \approx 11.95 cm^2 after\ calculating\ the\ square\ root[/tex]

Thus the area of the triangle is approximately [tex]11.95 cm^2[/tex] (rounded to two decimal places). Note that the question's original instructions to round to two significant figures would result in an answer of [tex]12 cm^2[/tex].

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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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:

Widest to narrowest

[tex]y=-\frac{1}{5}x^2[/tex] -  [tex]y=-\frac{1}{3}x^2[/tex] - [tex]y=-7x^2[/tex]                  

Step-by-step explanation:

Given :  Graph 1 - [tex]y=-7x^2[/tex]

Graph 2- [tex]y=-\frac{1}{5}x^2[/tex]

Graph 3 - [tex]y=-\frac{1}{3}x^2[/tex]

To find : Order the group of quadratic functions from widest to narrowest graph.

Solution :

First we plot the given graph,

Refer the attached figure below.

In the graph, we see that all graph has same vertices (0,0) and

Graph 2 with green in color  [tex]y=-\frac{1}{5}x^2[/tex] is the most widest graph among all.

Then graph 3 with purple in color is the widest and then graph 1 with blue in color is the most narrowest graph.

So, The order of the graph from widest to narrowest is

Graph 2 - Graph 3 - Graph 1

[tex]y=-\frac{1}{5}x^2[/tex] -  [tex]y=-\frac{1}{3}x^2[/tex] - [tex]y=-7x^2[/tex]

Answer:

4/15 is 100% the answer *NOT* 1/9 or anything else!

Step-by-step explanation:

To find the original price of Lisa's suit, convert the discount to a decimal and divide the sale price by one minus the discount rate. The original price is calculated to be $540.

To calculate the original price of Lisa's suit, which she bought on sale for $459 at a discount of 15% less than the original price, we can use the formula:

Original Price = Sale Price / (1 - Discount Percent)

First, we convert the percentage discount to a decimal:

15% = 0.15

Then, we divide the sale price by the complement of the discount rate:

Original Price = $459 / (1 - 0.15)
Original Price = $459 / 0.85
Original Price = $540

Therefore, the original price of the suit was $540.

The measure of ∠WZX is B; y, because Triangle UVW is similar to triangle ZXW.

The vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

We can see that Angles UVW ad ZXW are congruent,

Then because of the vertical angle theorem; angles UWV and XWZ are congruent.

So if there are 2 angles in each triangle which are congruent to each other, then the triangle angle sum theorem state that the third angle also has to be congruent in each.

BUT congruent angles do not make the triangles congruent due to the length of the sides can change and the measures of the angles remain unchanged.

Hence, The measure of ∠WZX is B; y, because Triangle UVW is similar to triangle ZXW.

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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

The statement that is true for the graph of function shown below is option (B) both graphs have exactly one asymptote is the correct answer.

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).

For the given situation,

The diagram shows the graph that has 2 functions f(x) and g(x).

The function f(x) is increasing function and the function g(x) is decreasing function.

An asymptote of a curve y = f (x) that has an infinite branch is called a line such that the distance between the point (x, f (x)) lying on the curve and the line approaches zero as the point moves along the branch to infinity.

Here the two functions f(x) and g(x) approaches zero at asymptote of 1.

Hence we can conclude that the statement that is true for the graph of function shown below is option (B) both graphs have exactly one asymptote is the correct answer.

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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}.

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 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 actual distance between the cities are 40 miles.

The scale factor states the scale or measurement by which a figure is bigger or smaller than the other figure. The size by which the figure would be reduced or enlarged is called its scale factor.

According to the question we are given that On a map, 1 inch equals 5 miles. two cities are 8 inches apart on the map.

that is, 1cm : 5 miles

Here two cities are 8 inches apart on the map.

then 8 inches equals to

5 x 8 = 40 miles.

The actual distance is 40 miles.

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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

12/5 = 2.4 times larger

3 x 2.4 = 7.2 inches wide