a cars fuel tank can hold 20 gallons of gas total it is only half full you stop and buy 5 gallons of gas how full is he fuel tank after you buy gas
a club has 15 members. How many ways can the club choose a president, vice president, and treasurer? (club rules forbid one person from holding more than one office.) show all work
There are 2730 different ways for a club with 15 members to choose a president, vice president, and treasurer, with each office being held by a different person.
Explanation:To determine the number of ways the club can choose a president, vice president, and treasurer, we can use the concept of permutations since the order of selection matters here, and no person can hold more than one office.
The first office to be filled is the president's.
There are 15 potential members to fill this role.
Once the president has been chosen, there are 14 remaining members who could be the vice president.
Finally, for the treasurer, there are 13 members left to choose from.
To find the total number of ways to choose these officers, we multiply the number of choices for each office together.
Number of ways = 15 (for president) × 14 (for vice president) × 13 (for treasurer) = 2730 ways.
So, there are 2730 different ways in which the club can select a president, vice president, and treasurer.
An equation that is true for all allowed values of the variable
perform the indicated operation 1/3 divide 3/8
Answer:
[tex]\frac{8}{9}[/tex]
Step-by-step explanation:
perform the indicated operation 1/3 divide 3/8
divide the fraction 1/3 and 3/8
When we divide the fractions, we flip the second fraction and multiply with first fraction.
[tex]\frac{\frac{1}{3} }{\frac{3}{8} }[/tex]
When we flip 3/8 it becomes 8/3
[tex]\frac{1}{3} \cdot \frac{8}{3}[/tex]
Multiply numerator with numerator and denominator with denominator
1 times 8 is 8
3 times 3 is 9
So final answer is [tex]\frac{8}{9}[/tex]
Theo budgets $154 for karate classes. He buys a karate uniform, called a dogi, for $12. If it costs $8 to attend each karate class, which inequality below represents the number of classes. c, that Theo can take?
Final answer:
The inequality representing the number of karate classes Theo can take is c ≤ 17, considering his budget after buying a dogi and the cost per class.
Explanation:
The question asks us to find the inequality that represents the number of karate classes, c, Theo can take given his budget scenario. Theo budgets $154 for his karate classes and spends $12 on a dogi. This leaves Theo with $154 - $12 = $142 for classes. Since each class costs $8, we divide the remaining budget by the cost per class to find the maximum number of classes he can take:
$142 ÷ $8 = 17.75.
Since Theo cannot attend a fraction of a class, we round down to 17. The inequality representing the number of classes Theo can take would be c ≤ 17, where c is the number of classes Theo can attend.
The inequality that represents the number of classes, [tex]\( c \)[/tex], that Theo can take is:
[tex]\[ 8c + 12 \leq 154 \][/tex]
To derive this inequality, we start by considering the total amount Theo has budgeted for karate classes, which is $154. From this budget, Theo has already spent $12 on purchasing a karate uniform. Therefore, the remaining amount available for attending the classes is [tex]\( 154 - 12 \)[/tex].
Now, each karate class costs $8, so the total cost for attending [tex]\( c \)[/tex] classes is [tex]\( 8c \)[/tex]. To ensure that Theo does not exceed his budget, the total cost including the uniform should be less than or equal to $154.
Hence, the inequality that represents this situation is:
[tex]\[ 8c + 12 \leq 154 \][/tex]
This inequality states that the cost of the uniform plus the cost of the classes must be less than or equal to Theo's budget. Solving for [tex]\( c \)[/tex] will give us the maximum number of classes Theo can attend without exceeding his budget.
Make a the subject of the formula:p=2a-3
After a busy day of orders, a florist has 6 roses, 7 lilies, 3 carnations, 35 chrysanthemums, 27 sunflowers, 18 violets, and 9 tulips left in her inventory. part
a.write a ratio that compares the number of roses to the number of violets. part
b.describe what three other comparisons have the same ratio. part
c.provide reasoning why more than one comparison can be made with the same ratio.
A student is using the completing the square method to transform the equation x2-10x+ 36 = 0 to the form (x-h) 2+k = 0. which step would give him the correct answer?
an interval has the notation (-9,-7). find the distance from the midpoint of the interval to either end point
The area of triangle ABC is 24 square centimeters. If B = 30° and a = 6 cm, what is the measure of side c? 4 cm 8 cm 16 cm 32 cm
Answer:
16 cm
Step-by-step explanation:
Given : The area of triangle ABC is 24 square centimeters.
To Find: If B = 30° and a = 6 cm, what is the measure of side c?
Solution:
Formula : [tex]Area = \frac{1}{2} \times a \times c \times sin B[/tex]
a = 6
Area = 24
B = 30°
Substitute the values in the formula
[tex]24 = \frac{1}{2} \times 6 \times c \times sin 30[/tex]
[tex]24 = \frac{1}{2} \times 6 \times c \times \frac{1}{2}[/tex]
[tex]24 =3 \times c \times \frac{1}{2}[/tex]
[tex]\frac{24 \times 2}{3} =c[/tex]
[tex]16=c[/tex]
Hence the measure of side c is 16 cm
So, Option c is correct.
The surface areas of two similar cones are 20 ft^2 and 125 ft^2. What is the scale factor?
A. 1/5
B. 2/5
C. 3/5
D. 4/5
The scale factor between two similar cones with surface areas of 20 ft² and 125 ft² is found by taking the square root of the ratio of the surface areas, which is [tex]\frac{1}{6.25}[/tex], resulting in a scale factor of B. [tex]\frac{2}{5}[/tex].
The question is asking about the scale factor between two similar cones with given surface areas. In the case of similar figures, the ratio of their surface areas is equal to the square of the scale factor. To find the scale factor, we take the square root of the ratio of the surface areas.
First, find the ratio of the surface areas: surface area of smaller cone : surface area of larger cone = [tex]\frac{20 ft^2}{125 ft^2}[/tex] = [tex]\frac{1}{6.25}[/tex].
Then, we take the square root of the ratio to find the scale factor: [tex]\sqrt{ (\frac{1}{6.25})}[/tex] = [tex]\frac{1}{2.5}[/tex], which simplifies to [tex]\frac{2}{5}[/tex]. Therefore, the scale factor is [tex]\frac{2}{5}[/tex], making option B the correct answer.
To find the scale factor between two similar cones, you can use the ratio of their corresponding lengths.
The surface area of a cone is proportional to the square of its height.
Let's denote the scale factor as kk. If A1A1 and A2A2 are the surface areas of the first and second cone respectively, then:
A1/A2=(k/1)^2
Given A1=20 ft^2 and A2=125 ft^2, we have:
20/125=(k/1)^2
Solving for k:
k= √ 20/125=√ 4/25=2/5=52
So, the correct answer is B. 2/5
complete question;
The surface areas of two similar cones are 20 ft^2 and 125 ft^2. What is the scale factor?
A. 1/5
B. 2/5
C. 3/5
D. 4/5
Is 23 a prime number or a composite number? Plzz help
Find the exponential function f(x)=ca^x given two points (1,6) (3,24)
The exponential function is f(x) = 3(2)× which is passes throgh the two points (1,6) and (3,24).
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x
where a is a constant and a>1
We have:
An exponential function:
f(x) = c(a)×
The two points are given:
(1,6) and (3,24)
Plug x = 1
f(x) = 6
6 = c(a) ...(I)
Plug x = 3
f(x) = 24
24 = c(a)³ ...(II)
Divide equations (1) and (II)
24/6 = c(a)³/c(a)
4 = a²
a = 2
Plug a = 2 in equation I
6 = c(2)
c = 6/2
c = 3
The exponential function:
f(x) = 3(2)×
Thus, the exponential function is f(x) = 3(2)× which is passes throgh the two points (1,6) and (3,24).
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Suppose that a stove and a freezer together weigh at least 370 pounds. The weight of the stove is 170 pounds. Which inequality correctly describes these conditions for the weight of the freezer,
The inequality representing the weight of the freezer when the stove weighs 170 pounds and the combined weight of both is at least 370 pounds is 170 + F ≥ 370.
To find the correct inequality for the weight of the freezer, given that the stove weighs 170 pounds and the combined weight of the stove and freezer is at least 370 pounds, you can represent this as an inequality.
Let F represent the weight of the freezer.The inequality that correctly describes the conditions is:170 + F ≥ 370
In this inequality, 170 represents the weight of the stove and F represents the weight of the freezer.
Therefore, the correct inequality is 170 + F ≥ 370.
Graph the solution of 2 ≥ 4 - v
Answer:
Ok so ppl it just A
Step-by-step explanation:
To solve this problem, we must first subtract 4 from both sides of the inequality. This gives us -2 ≥ -v. Next divide both sides by -1. Remember, when you divide by a negative in an inequality, it becomes necessary to flip the direction of the inequality symbol. Therefore, the answer to the inequality is 2 ≤ v, which is equivalent to v ≥ 2.
A street light is mounted on a pole. The tip of the shadow of a man who is standing on a street a short distance from the pole has an angle of elevation to the top of his head of 28°. A woman standing in the opposite direction of the pole as the man was standing on the same street has a angle of elevation from the tip of her shadow to her head of 24°. If the two people are 20 feet apart, how far is the street light from the head of the woman?
(20 PTS!!)
The dot plot below shows the amount of time two random groups of students took to brush their teeth:
Based on visual inspection of the dot plots, which of the following groups, if any, shows a greater average time required to brush their teeth?
Group R
Group S
Both groups show about the same average time.
No conclusion about average time can be made from the data.
Answer:
The correct option is C.
Step-by-step explanation:
In a dot plot, the number of dots above a number represents the frequency of that number.
From the given dot plot it is clear that number of dots for group R is 21 and the time taken by the students of groups R are
45, 50, 50, 55, 60, 60, 70, 75, 80, 85, 90, 90, 95, 100, 100, 105, 110, 110, 115, 120, 120
The average of the data is
[tex]Average=\frac{\sum x}{n}[/tex]
[tex]Average=\frac{45+50+50+55+60+60+70+75+80+85+90+90+95+100+100+105+110+110+115+120+120}{21}[/tex]
[tex]Average=\frac{1785}{21}[/tex]
[tex]Average=85[/tex]
From the given dot plot it is clear that number of dots for group S is 17 and the time taken by the students of groups S are
50, 55, 60, 60, 65, 70, 70, 80, 90, 90, 95, 100, 105, 110, 110, 115, 120
[tex]Average=\frac{50+55+60+60+65+70+70+80+90+90+95+100+105+110+110+115+120}{17}[/tex]
[tex]Average=\frac{1445}{17}[/tex]
[tex]Average=85[/tex]
The average time of both groups are same.
Since both groups show about the same average time, therefore the correct option is C.
Write a percent proportion for which the percent is greater than 100 and the part is known. Use the percent equation to solve your problem to find the whole.
yepAnswer:
Step-by-step explanation:
What is the approximate surface area of the sphere 15yd?
A: 225 yd^2
B: 707 yd^2
C: 1,767 yd^2
D: 5,301 yd^2
The approximate surface area of the sphere will be 707 yd^2
What is sphere?Sphere is a round solid figure, or its surface, with every point on its surface equidistant from its centre.A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. How to solve this problem?The steps are as follow:
Given the diameter of sphere is 15 ydSo the radius will be half of diameter which will be 7.5 ydThe surface area of sphere will be as follow:r = 7.5 yd
Surface area of sphere = 4πr^2
Surface area of sphere = 4*π*(7.5)^2
Surface area of sphere = 706.85 yd^2
Surface area of sphere = 707 yd^2
So the approximate surface area of the sphere will be 707 yd^2
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11) Write the equation of the circle with center (7, 3) and a radius of 2.
Answer:
(x - 7)² + (y - 3)² = 4
Step-by-step explanation:
The equation formula of a circle is (x - h)² + (y - k)² = r², where the center is at ordered pair (h, k) and r represents the radius in units.
With the information given in the question itself, we plug and play, simplifying if need be:
center (7, 3), h = 7, k = 3
radius = 2
(x - 7)² + (y - 3)² = (2)²
(x - 7)² + (y - 3)² = 4
The equation of this circle is (x - 7)² + (y - 3)² = 4
A weight attached to a spring is at its lowest point, 9 inches below equilibrium, at time t = 0 seconds. When the weight it released, it oscillates and returns to its original position at t = 3 seconds. Which of the following equations models the distance, d, of the weight from its equilibrium after t seconds?
a. d=-9cos(pi/3)t
b. d=-9cos(2pi/3)t
c. d=-3cos(pi/9)t
d. d=-3cos(2pi/9)t
For a better understanding of the explanation provided here kindly go through the file attached.
Since, the weight attached is already at the lowest point at time, t=0, therefore, the equation will have a -9 as it's "amplitude" and it will be a Cosine function. This is because in cosine function, the function has the value of the amplitude at t=0.
Now, we know that the total angle in radians covered by a cosine in a given period is [tex] 2\pi [/tex] and the period given in the question is t=3 seconds. Therefore, the angular velocity, [tex] \omega [/tex] of the mentioned system will be:
[tex] \omega=\frac{2\pi}{3} [/tex]
Combining all the above information, we see that the equation which models the distance, d, of the weight from its equilibrium after t seconds will be:
[tex] d=-9cos(\frac{2\pi}{3})t [/tex]
Thus, Option B is the correct option. The attached diagram is the graph of the option B and we can see clearly that at t=3, the weight indeed returns to it's original position.
Answer: B.
Step-by-step explanation:
answer on edge
Pls explain 4 brainliest!
May the 4th be with you
If f(x) = 5x, what is f–1(x)?
Rewrite the equation below so that it does not have fractions.2/3x-3=3/4Do not use decimals in your answer
The equation without fractions is 8x - 36 = 9.
To eliminate fractions from the equation 2/3x - 3 = 3/4, you can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 12:
(12) * (2/3x - 3) = (12) * (3/4)
This will clear the fractions:
2(4x) - 3(12) = 3(3)
Now, simplify each term:
8x - 36 = 9
So, the equation without fractions is:
8x - 36 = 9
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50 POINTS!!!!
-
The Dust Bowl hit middle America a few years after the Great Depression started, and the Dust Bowl was considered one of the causes that continued the Great Depression during the 1930’s. Explain in three sentences how this natural disaster affected America’s economy in the 1930’s?
what is the y-coordinate of the vertex of the function y=2x^2+5x-8
George has a lawn care business. He charges $70.00 per yard that he cuts. It costs George $3.49 per yard for lawn mower maintenance and $24.04 per yard for gasoline. Approximately how much profit will George make if he cuts 6 yards? A. $402.00 B. $582.00 C. $276.00 D. $258.00
Find the number of real number solutions for the equation. x^2 + 5x + 7 = 0 0 cannot be determined 1 2
Answer:
No real solutions, or 0
Explanation:
We can determine how many real solutions a quadratic function has, we can use the quadratic formula.
The quadratic formula for expressions written in ax² + bx + c form is:
[tex]x = \frac{-b +/- \sqrt{b^{2}-4ac}}{2a}[/tex]
In the equation x² + 5x + 7, a = 1, b = 5 and c = 7
When we plug them in, we get:
[tex]x = \frac{-5 +/-\sqrt{5^2 - 4(1)(7)}}{2(1)}\\ \\= \frac{-5+/-\sqrt{25 - 28}}{2}\\ \\=\frac{-5+/-\sqrt{-3}}{2}}[/tex]
We cannot find the square root of a negative number without diving into the realm of imaginary numbers in which √-3 becomes i√3. Therefore, the equation has no real solutions. This is because the equation x² + 5x + 7 is an upward-facing parabola translated up 7 units and, as such, does not cross the x-axis. If the equation yields a graph that does not cross the x-axis, then there will be zero answers for what variable x equals.
An instructor makes $15 more per hour than an assistant. If the combined hourly wage of the instructor and assistant is $65, what is the hourly wage of the assistant? A. $15 B. $20 C. $25 D. $30
Which algebraic rule describes the 180° counterclockwise rotation about the origin
Answer:
[tex](x,y)\rightarrow (-x,-y)[/tex]
Step-by-step explanation:
We are asked to find the the algebraic rule describes the 180° counterclockwise rotation about the origin .
We know that when we rotate a point 180° counterclockwise rotation about the origin , the x and y-coordinates change their sign.
[tex](x,y)\rightarrow (-x,-y)[/tex]
Therefore, our required rule is [tex](x,y)\rightarrow (-x,-y)[/tex].