A bag contains 4 green, 3 blue, and 5 yellow marbles. What is the probability of selecting a green marble, replacing it, then selecting a yellow marble?
Answer:
5/36
Step-by-step explanation:
Total number in the universe = 4 + 3 + 5 = 12Probability of selecting a green (first time) = 4/12Probability of selecting a yellow (2nd time) = 5/12P(gr then yellow) = 4/12 * 5/12 = 20 / 144This reduces to 5/36Mario is setting up a new tent during a camping trip. The tent came with 7 feet of rope. The instructions are to use 34.5 inches of rope to tie a tarp on top of the tent. Then the remaining rope should be cut into 8 1/4 inches sections to tie a tent to states in the ground. Mario will use all the rope as instructed. Determine the number of 8 1/4 inch sections of rope mario can cut from the rope.
Answer: There are 6 sections of [tex]8\frac{1}{4}\ inches[/tex] of rope Mario can cut from the rope .
Step-by-step explanation:
Since we have given that
Length of the rope for the tent = 7 feet
As we know that
[tex]1\ feet=12\ inches\\\\7\ feet=12\times 7=84\ inches[/tex]
Length of rope is used to tie a tarp on top of the tent = 34.5 inches
Remaining length of rope is given by
[tex]84-34.5=49.5\ inches[/tex]
According to question, the remaining rope should be cut into
[tex]8\frac{1}{4}\ inches\\\\=\frac{33}{4}\ inches[/tex]
So, Number of [tex]8\frac{1}{4}\ inches[/tex] sections of rope Mario can cut from the rope is given by
[tex]\frac{49.5}{8\frac{1}{4}}\\\\=\frac{49.5}{\frac{33}{4}}\\\\=\frac{49.5\times 4}{33}\\\\=6[/tex]
Hence, there are 6 sections of [tex]8\frac{1}{4}\ inches[/tex] rope Mario can cut from the rope .
Answer:
6
Step-by-step explanation:
Mario has 7 feet of rope. Since there are 12 inches in every foot, this means he has
7(12) = 84 inches of rope.
34.5 inches of the rope must be used to tie the tarp to the top; this leaves Mario with
84-34.5 = 49.5
This remaining rope will be cut into 8 1/4 inch sections. We can also write 8 1/4 as 8.25. To find the number of sections this length he can cut, we divide:
49.5/8.25 = 6
He can cut 6 sections this length.
Last week Kelly ran 20 miles this week she ran 32 miles what was the percent change in the number of miles she ran
Homer Simpson finds himself in a panic attempting to meet the April 15th tax deadline. If Homer and his wife have an income of $60,000, earned $1200 in interest, invested $2500 in a tax-deferred savings plan, and have a total of $12,000 in exemptions and deductions, what would be his taxable income
After all the deductions and exemptions, the total taxable income of Homer Simpson is $46,700.
Given that, income of Homer and his wife = $60000 and interest earned = $1200.
In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.
Adding this to total income, we have total taxable amount = 60000+1200 = $61200
Now, investment in tax deferred savings plan = $2500
This amount will be subtracted from total taxable income, so amount becomes = 61200-2500 = $58700
Subtract the exemptions and deductions = $12000
That is, amount becomes = 58700-12000 = $46700
Hence, the net taxable income is $46,700.
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Homer Simpson's taxable income is determined by subtracting his tax-deferred savings and total deductions from his total income. His taxable income comes to $46,700. The percentage of tax he pays depends on the U.S income tax bracket he falls under.
Explanation:To calculate Homer Simpson's taxable income, we need to consider their total income, deductions, and investments. Homer's total income is the sum of his salary, $60,000 and the interest earned, $1200. So, the total income equals $60,000 + $1200 = $61,200.
Next, we subtract the total deductions which include the tax-deferred savings plan and the total deductions and exemptions they have, from the total income. Thus, the taxable income equals $61,200 - $2,500 (savings plan) - $12,000 (deductions and exemptions) = $46,700.
The U.S income tax code is based on a progressive system, so knowing the taxable income can help determine the income tax bracket Homer falls under. Given the figures, Homer's income is in the bracket that is taxed at 22% as per the 2020 basic tax tables from the Internal Revenue Service. However, it is important to take into consideration any changes in tax laws or additional deductions they might have.
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In triangle ABC, m<A=80, m<B=50, AB=4x-4, AC=2x+16, BC=5x+4. Find BC
Answer:
BC - 54 units
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
∠C = 180° - (∠A + ∠B) = 180° - (80 + 50)° = 180° - 130° = 50°
Since ∠B = ∠C = 50° then the base angles of the triangle are equal hence the triangle is isosceles with
AB = AC, that is
4x - 4 = 2x + 16 ( subtract 2x from both sides )
2x - 4 = 16 ( add 4 to both sides )
2x = 20 ( divide both sides by 2 )
x = 10
⇒ BC = 5x + 4 = (5 × 10) + 4 = 50 + 4 = 54
If she completely guesses on all of the questions, what is the probability that she gets two of the four questions correct?
Answer:
D) 0.211
Step-by-step explanation:
The probability of getting a correct answer is 1/4, so the probability of an incorrect answer is 3/4.
The probability of 2 correct and 2 incorrect is (1/4)(1/4)(3/4)(3/4) = 9/256.
There are C(4,2) = 4·3/(2·1) = 6 ways to have some combination of 2 correct and 2 incorrect out of 4 questions. So, the probability of that result is ...
... 6 · 9/256 = 27/128 =0.2109375 ≈ 0.211
50 points Hannah is 2 times her sister’s age. The sum of their ages is no more than 18 years.
1) Write an inequality that can be used to represent this situation.
2) Using the inequality you just found, solve it to find the oldest age Hannah's sister can be.
Answer:
Step-by-step explanation:
Let "Hannah" = h, and her sister = s
h = 2s
h + s ≤ 18
Plug in 2s for h in the second equation.
(2s) + s ≤ 18
Simplify
2s + s ≤ 18
3s ≤ 18
Isolate the variable (s). Divide 3 from both sides
(3s)/3 ≤ (18)/3
s ≤ 18/3
s ≤ 6
2) The oldest Hannah's sister can be is 6 years
~
Answer:
12 years old
Step-by-step explanation:
1) 2x+x=18
2) Now solve 2x+x=18
Add alike terms
3x=18
Now divide both sides by 3 (3x/3 and 18/3)
x=6
So Hannah is 6 years old. Her sister must be 12.
In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, AE=x2−16 , and CE=6x .
What is AC ?
Enter your answer in the box.
_______units
Answer:
AC is 96 units
Matt is making a scale model of a building the model is 3.4 feet tall the actual building is 41.848 ft tall.How many times as great is the actual building as the model
41.848/3.4=12.308
The actual building is 12.306 times larger than the model.
A person standing close to the edge on top of a 112-foot building throws a ball vertically upward. The quadratic function h ( t ) = − 16t^2 + 96t + 112 models the ball's height about the ground, h ( t ) , in feet, t seconds after it was thrown.
a) What is the maximum height of the ball?
b) How many seconds does it take until the ball hits the ground?
Answer:
the maximum height of the ball= 256 feet
7 seconds
Step-by-step explanation:
The quadratic function h ( t ) = − 16t^2 + 96t + 112 models the ball's height about the ground, h ( t ) , in feet, t seconds after it was thrown.
a= -16 , b= 96 and c= 112
To find maximum height , we find vertex
[tex]x= \frac{-b}{2a}=\frac{-96}{2(-16)}= 3[/tex]
Now plug in 3 for 't' in h(t)
[tex]h(t) = -16t^2 + 96t + 112[/tex]
[tex]h(t) = -16(3)^2 + 96(3)+ 112=256[/tex]
Hence vertex is (3, 256)
the maximum height of the ball= 256 feet
(b) when the ball hits the ground then height becomes 0
so we plug in 0 for h(t) and solve for t
[tex]0 = -16t^2 + 96t + 112[/tex]
Apply quadratic formula
[tex]t=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
Plug in all the values a= -16 , b= 96 and c= 112
[tex]t=\frac{-96+-\sqrt{96^2-4(-16)(112)}}{2(-16)}[/tex]
t= -1 and t= 7
time cannot be negative. So it will take 7 second to hit the ground.
The maximum height of the ball is 160 feet and it takes 4 seconds for the ball to hit the ground.
Explanation:The quadratic function h(t) = -16t^2 + 96t + 112 represents the height of the ball above the ground (h(t)) in feet after t seconds since it was thrown. To find the maximum height of the ball, we need to determine the vertex of the quadratic function. The vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by the formula x = -b/2a, where x represents the time and a and b are coefficients in the quadratic equation.
In this case, the coefficient a = -16 and b = 96. Plugging these values into the formula, we get t = -96/(2 * -16) = 3 seconds. Substituting this value into the quadratic function, we find h(t) = -16(3^2) + 96(3) + 112 = 160 feet. Therefore, the maximum height of the ball is 160 feet.
To determine how many seconds it takes until the ball hits the ground, we need to find the time when h(t) = 0. Setting the quadratic equation equal to zero and solving for t, we get -16t^2 + 96t + 112 = 0. This equation can be solved using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula.
Applying the quadratic formula, we have t = (-b ± √(b^2 - 4ac)) / 2a. Plugging in the values of a = -16, b = 96, and c = 112, we get t = (-96 ± √(96^2 - 4(-16)(112))) / (2 * -16). Evaluating this expression, we get two solutions: t = 4 and t = 7. Therefore, the ball takes 4 seconds to reach the ground after being thrown.
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!really need help fast
I'm really sorry that I took a long time. I got carried away. Hopefully my work was correct though.
A= about 354 square feet~ (rounded)
The stage can be split into two shapes. The first is a trapezoid and the formula to find the area for it would be A=(b₁+b₂)/2 and then multiple by the height. b₁ would be 17 and b₂ is 20 and the height is 13. 17+20 is 37. 37/2 is 18.5. 18.5 times 13 is 240.5. Area of the trapezoid is 240.5 square feet. Then we need to find the area of the semicircle. The formula is A=(πr²)2. r is the radius which is half of the diameter. The diameter is 17 so the radius is 8.5. π is about 3.14 if you don't have a calculator. 8.5 squared is 72.25. 72.25 times 3.14 is 226.865. 226.865/2 is 113.4325. The area of the half circle is 113.4325. Just add these two areas to get 353.9325. So I think the area is pretty much 353.9325 but might be slightly different because some values I said were rounded. Either way the answer should be similar.
I forgot you said you needed help fast and got carried away. Sorry if I wasn't fast enough and hopefully I did my math correctly.
The sale tax on the purchase of a refrigerator that cost 695 is 7 percent.What is the amount of sales tax
∆ABC is transformed with the center of dilation at the origin.
Pre-image: ∆ABC with vertices A(−3, 4), B(−1, 12), C(4, −2)
Image: ∆A'B'C' with vertices A' (−0.6, 0.8), B' (−0.2, 2.4), C' (0.8, −0.4)
What is the scale factor of the dilation that maps the pre-image to the image?
Answer:
1/5
Step-by-step explanation:
We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(−3, 4), B(−1, 12) and C(4, −2) to the image triangle A'B'C' with vertices A' (−0.6, 0.8), B' (−0.2, 2.4) and C' (0.8, −0.4).
Center of dilation is at the origin.
To find the scale factor, we will divide the corresponding vertices of the image and pre-image.
A (−3, 4) ---> A' (−0.6, 0.8) = [tex]\frac{-0.6}{-3} , \frac{0.8}{4}=(\frac{1}{5} , \frac{1}{5})[/tex]
B(−1, 12) ---> B' (−0.2, 2.4) = [tex]\frac{-0.2}{-1} , \frac{2.4}{12} = (\frac{1}{5} , \frac{1}{5})[/tex]
C(4, −2) ---> C' (0.8, −0.4) = [tex]\frac{0.8}{4} , \frac{-0.4}{-2} = (\frac{1}{5} , \frac{1}{5})[/tex]
Therefore, the scale factor of the dilation is 1/5.
If two sides of a triangle are 3cm and 5cm in length, which could not be the measure of the third side ?
Answer: c-5 cm, 2 cm, 2 cm.
Gene paid $171 to keep his dog at the kennel for 12 days. What was the unit rate, r, per day to keep the dog at the kennel?
Final answer:
The unit rate, r, per day to keep the dog at the kennel is $14.25.
Explanation:
To find the unit rate, we need to divide the total cost by the number of days. In this case, Gene paid $171 to keep his dog at the kennel for 12 days. So the unit rate, which represents the cost per day, is calculated as:
Unit rate = Total cost / Number of days
Unit rate = $171 / 12
Unit rate = $14.25 per day which is the required answer
Therefore, unit rate to keep the dog at the kennel is $14.25 per day.
A metal alloy is made by mixing 12 ounce of metal C with 13 ounce of metal D. What is the total weight of the alloy?
Answer:
25 ounces.
Step-by-step explanation:
We have been given that a metal alloy is made by mixing 12 ounce of metal C with 13 ounce of metal D.
To find the total weight of the alloy we will add the weight of metal C and weight of metal D.
[tex]\text{The total weight of the alloy}=\text{Weight of metal C + Weight of metal D}[/tex]
[tex]\text{The total weight of the alloy}=12\text{ ounce}+13\text{ ounce}[/tex]
[tex]\text{The total weight of the alloy}=25\text{ ounce}[/tex]
Therefore, the total weight of alloy is 25 ounces.
Answer:
5/6 is your correct answer..
Step-by-step explanation:
The graph shows the function f(x).
What is the function's average rate of change from x=−1
to x = 2?
Enter your answer, as a simplified fraction, in the boxes.
Answer:
Need the graph for final answer. Use the values of the graph to substitute into the slope formula and simplify.
Step-by-step explanation:
The average rate of change is the amount over an interval the outputs change in a ratio to the input change. In a linear function, this is constant and called slope. In all other function, it is called the average rate of change because the rate of change varies over the interval. We use the same formula for the average rate of change as we do slope. First we need both the input and output values of the function over the interval.
Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values for your function into the slope formula and simplify.
Answer:
is there a graph
Step-by-step explanation:
What is the exact value of 7^x x=2 ?
Pre-calc show your work.
Answer:
49
Step-by-step explanation:
7^x
If x=2
7^2
49
Use a calculator to find the approximate value of the expression. Round the answer to two decimal places. The cosine of the complimentary angle to 58° a. 0.74 c. 0.83 b. 0.85 d. 0.94 Please select the best answer from the choices provided A B C D
Answer:
B) 0.85
Step-by-step explanation:
By definition, complementary angles add to 90 degrees.
The given angle 58 degrees is complementary to 90-58 = 32 degrees. The two angles 58 and 32 add to 90.
Therefore, cos(32) = 0.848 = 0.85
The complementary angle to 58° is 42° and the cosine value of 42° is 0.74.
What is Complementary Angles?Two angles are said to be complementary when the sum of those two angles add up to 90°.These angles can be adjacent to each other or not.For two complementary angles, each angle is a complement of other.Given: angle 58°.
let the angle complementary to 58° be x.
By the definition of complementary angles, we can write:
⇒ x + 58° = 90°
⇒ x = 90° - 58°
⇒ x = 42°
Therefore, the angle complementary to 58° is 42°.
Now, we have to find the cosine value of 42°.
⇒ cos (42°) = 0.74
Therefore, the cosine value of 42° that is the complementary angle to 58° is 0.74.
Hence, the best answer will be option (A).
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find the value of x.
a) 18
b) 6
c) 15
d) 7
Answer:
b) 6
Step-by-step explanation:
Since this is an isosceles triangle, the two sides are equal and the two angles are equal.
That means
5x-3 = 2x+15
Subtract 2x from each side.
5x-2x-3 = 2x-2x+15
3x-3 = 15
Add 3 to each side.
3x-3+3 = 15+3
3x =18
Divide each side by 3
3x/3 = 18/3
x =6
Answer: the answer to this question is A because the angle is acute angle and when you solve (5x-3) it equals up to 18 when you finish figureing it out.
Step-by-step explanation:
At 6:00 AM there where 400 gallons of water in the pool.At 11:00 AM there were 2400 gallons of water in the pool. What is the rate of change of water in the pool?
Answer:
The rate of change of water in the pool is 400 gallons / hour
Step-by-step explanation:
We are given
At 6:00 AM:
there were 400 gallons of water in the pool
so,
[tex]N_1=400[/tex]
At 11:00 AM:
there were 2400 gallons of water in the pool
so,
[tex]N_2=2400[/tex]
now, we can find time between
t=11-6=5 hours
now, we can use formula
rate of change of water in pool is
=( change in water quantity)/( total time)
so, we get
[tex]=\frac{N_2-N_1}{t}[/tex]
now, we can plug values
[tex]=\frac{2400-400}{5}[/tex]
[tex]=\frac{2000}{5}[/tex]
[tex]=400[/tex]
So,
The rate of change of water in the pool is 400 gallons / hour
Below is a graph of exponential functions label I though VI.
Answer:
option-C
Step-by-step explanation:
We are given
graphs -- I , V , VI have same starting point
it means that it has same initial values
Suppose, we are given exponential function as
[tex]f(x)=a(b)^x[/tex]
Here , 'a' is initial value
we can see that initial value of graph-I is 30
so, all other graphs must also have 30 initial value
so, graphs
[tex]e,\delta , \phi[/tex] have same initial value =30
so, option-C.......Answer
Anja divides (8x3 – 36x2 + 54x – 27) by (2x – 3) as shown below. What error does Anja make? 2x-3sqrt 4x^-12x+9/8x-36x^2+54x-27
THE ANSWER IS C
Answer:
c
Step-by-step explanation:
What is the solution to the equation x+3/x+2=3+1/x
Answer:
x=-1
Step-by-step explanation:
x+3
------- = 3 + 1/x
x+2
Get a common denominator on the right
3*x/x + 1/x
3x/x + 1/x = (3x+1)/x
x+3 3x+1
------- = ---------
x+2 x
We can use cross products to solve
(x+3) *x = (3x+1) * (x+2)
x^2+3x = 3x*x +x + 3x*2 +2
Simplifying
x^2 + 3x = 3x^2 +7x+2
Subtract x^2 from each side
x^2 -x^2 + 3x = 3x^2-x^2 +7x+2
3x = 2x^2 +7x+2
Subtract 3x from each side
3x-3x = 2x^2 +7x -3x+2
0 = 2x^2 +4x +2
Divide by 2
0 = x^2 +2x +1
Factor
0 = (x+1) (x+1)
Using the zero product property
x+1 =0
x=-1
Answer:
The solution set is { -1 }.
Step-by-step explanation:
If we multiply each term by the LCM of x and x+ 2 ( = x(x + 2)) we get:-
x(x + 3) = 3x(x + 2) + x + 2
x^2 + 3x = 3x^2 + 6x + x + 2
0 = 3x^2 - x^2 - 3x + 6x + x + 2
2x^2 +4x + 2 = 0
2(x^2 + 2x + 1) = 0
2( x + 1)(x + 1) = 0
x = -1 Multiplicity 2
The solution set only contains 1 * -1 . Elements in a set are not repeated
So its {-1} (answer)
11) Flowers grow rapidly. A flower is 60 inches tall. Tomorrow it will be 71 inches tall. The next day it will be 82 inches tall, and on the next day it will be 93 inches tall. Write a rule to represent the height of the flower as an arithmetic sequence. How tall will the plant be in 12 days?
Answer:
you add 11 inches each day
Step-by-step explanation:
What is the solution set of the equation 8/q+2= q+4/q-1?
q=4,-1
you need to isolate q
The solution set of the equation is {-4, 2}
Given expression:
[tex]\frac{8}{q} +2=\frac{q+4}{q-1}[/tex]
Solve for q: simplify
[tex]\frac{8}{q} +2=\frac{q+4}{q-1}\\\frac{8+2q}{q}=\frac{q+4}{q-1}\\(8+2q)(q-1)=(q(q+4)\\8q-8+2q^{2} -2q=q^{2} +4q\\2q^{2} +6q-8 =q^{2}+4q\\q^{2} +2q-8=0[/tex]
Factorize the quadratic equation to solve q
[tex]q^{2} +4q-2q-8=0\\q(q+4)-2(q+4)=0\\(q+4)=0, (q-2)=0\\q= -4, 2[/tex]
Therefore, The solution set of the equation is {-4, 2}
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A pro basketball player has a vertical leap of 3333 in. What is his hang time? (Use V=48T2.)
Answer:
Hang time of the basketball player is 0.83 sec.
Step-by-step explanation:
A pro basketball player has a vertical leap of 33 in.
His hang-time can be calculated by the function given by,
[tex]V=48t^2[/tex]
Where,
V = vertical leap (vertical leap is the act of raising itself in the vertical plane)
t = the time for which the object stays in the air
Putting all the values,
[tex]\Rightarrow 33=48t^2[/tex]
[tex]\Rightarrow t^2=\dfrac{33}{48}[/tex]
[tex]\Rightarrow t=\sqrt{\dfrac{33}{48}}[/tex]
[tex]\Rightarrow t=0.83\ sec[/tex]
Therefore, hang time of the basketball player is 0.83 sec.
The selling price of an item is ?$ 440 440. It is marked down by 20?%, but this sale price is still marked up from the cost of ?$ 320 . Find the markup from cost to sale price.
To find the markup from cost to sale price, calculate the original sale price by dividing the selling price by (1 - discount percentage) which is 230
Explanation:To find the markup from cost to sale price, we first need to calculate the cost price.
The item is marked down by 20% from the selling price of $440.
So, the original sale price before the discount would be $440 / (1 - 0.20) = $550.
Since the sale price is still marked up from the cost of $320, we can calculate the markup as:
$550 - $320 = $230.
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Which of the following are remote interior angles of one check all that apply?
Answer:
<4 and <3
Step-by-step explanation:
The remote interior angles are the two angles that are inside the triangle and away from the angle adjacent to the exterior angle.
5 is adjacent to 1
so 3 and 4 are the remote interior angles
The baseball team sold $1,340 in tickets one Saturday. The number of $12 adult tickets was 15 more than twice the number of $5 child tickets. How many of each were sold?
Final answer:
40 child tickets and 95 adult tickets were sold.
Explanation:
Let's assume the number of child tickets sold is x.
According to the problem, the number of adult tickets sold is 15 more than twice the number of child tickets. So the number of adult tickets sold is 2x + 15.
The total income from ticket sales is $1,340. The income from child tickets is $5 times the number of child tickets and the income from adult tickets is $12 times the number of adult tickets.
Therefore, we can express the total income as the sum of the income from child tickets and adult tickets:
$5x + $12(2x + 15) = $1,340
Simplifying the equation:
$5x + $24x + $180 = $1,340
$29x = $1,340 - $180
$29x = $1,160
Dividing both sides by 29:
x = $1,160/$29
x = 40
So, the number of child tickets sold is 40, and the number of adult tickets sold is 2x + 15 = 2(40) + 15 = 80 + 15 = 95.
Therefore, 40 child tickets and 95 adult tickets were sold.