Using the properties of exponents:
5. The value of x is 9
6. The value of b is -4
7. The value of n is 0
Calculating exponentsFrom the question, we are to calculate the value of the exponent in each question
5.
8² · 8ˣ = 8¹¹
Applying the multiplication law of indices, this can be written as
8² ⁺ ˣ = 8¹¹
Equate the powers
2 + x = 11
Solve for x by subtracting 2 from both sides
2 - 2 + x = 11 - 2
x = 9
6.
5⁷ · 5ᵇ = 5³
Applying the multiplication law of indices, this can be written as
5⁷ ⁺ ᵇ = 5³
Equate the powers
7 + b = 3
Solve for b by subtracting 7 from both sides
7 - 7 + b = 3 - 7
b = -4
7.
x¹² · xⁿ = x¹²
Applying the multiplication law of indices, this can be written as
x¹² ⁺ ⁿ = x¹²
Equate the powers
12 + n = 12
Solve for n by subtracting 12 from both sides
12 - 12 + n = 12 - 12
n = 0
Hence, the value of n is 0
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Ivan created a scale drawing of the Grand Canyon using a scale of 1 inch for every 25
miles. His drawing is 11 inches long. What is the actual length of the canyon?
Answer:
275 miles
Step-by-step explanation:
Samantha is told that sin (O) = and tan (0)<0, and was asked to determine the value of cos (©).
• She uses the Pythagorean identity and defines it to be sin() + cos2 ( 0 )= 1.
• She substitutes į into the equation for sin (0)
• She then looks at values of sin ( ) and tan () and says that the only quadrant in which sin() is positive and
tan() is negative is the first quadrant.
Samantha determines that the answer is
cos () =
(21)
Samantha determines the answer as cos(θ) = -√(3/4).
Based on the information given, I can help you with this problem. Samantha is correct in using the Pythagorean identity and substitution, but she made an error in identifying the quadrant. Here's the correct process:
1. Given sin(θ) = 1/2 and tan(θ) < 0.
2. The correct quadrant where sin(θ) is positive and tan(θ) is negative is the second quadrant, not the first.
3. Using the Pythagorean identity: sin^2(θ) + cos^2(θ) = 1.
4. Substitute sin(θ) = 1/2 into the equation: (1/2)^2 + cos^2(θ) = 1.
5. Simplify: 1/4 + cos^2(θ) = 1.
6. Solve for cos^2(θ): cos^2(θ) = 3/4.
7. Since we are in the second quadrant, cos(θ) is negative: cos(θ) = -√(3/4).
Your answer: cos(θ) = -√(3/4).
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Malachi ask students in his class, “ how long does it take you to get to school?“ The histogram shows the data
Answer: C Distribution is symmetric
Step-by-step explanation:
Casey is going to wear a gray sportscoat and is trying to decide what tie he should wear to work. In his closet, he has 22 ties, 13 of which he feels go well with the sportscoat. If Casey selects one tie at random, determine the probability and the odds of the tie going well or not going well with the sportscoat.
The probability the tie goes well with the jacket is?
The probability the tie will not go well with the jacket is?
The odds against the tie going well with the jacket is?
(Simplify your answer. Type an integer or a fraction.)
The odds in favor of the tie going well with the jacket is?
(Simplify your answer. Type a ratio using a colon.)
A 2-quart carton of pineapple juice costs $8.08. What is the price per cup?
$
Answer:
$1.01
Step-by-step explanation:
We Know
A 2-quart carton of pineapple juice costs $8.08
1 quart = 4 cups
2 quarts = 8 cups
So, 8 cups of pineapple juice cost $8.08.
What is the price per cup?
We Take
8.08 / 8 = $1.01
So, the price per cup is $1.01
h=-16t^2+27t+3 what is the max height of the soccer ball
To find the maximum height of the soccer ball, we need to determine the vertex of the quadratic function. The vertex is given by the formula:
t = -b/2a
where a = -16 and b = 27 from the given equation:
H = -16t^2 + 27t + 3
Substituting these values into the formula, we get:
t = -27/(2(-16)) = 0.84375
Now that we have the value of t at the vertex, we can find the maximum height by substituting it back into the original equation:
H = -16(0.84375)^2 + 27(0.84375) + 3 = 12.65625
Therefore, the maximum height of the soccer ball is approximately 12.65625 units.
h = -16t^2 + 27t + 3 = -(4t - 27/8)^2 + 921/64
With every number t, h [tex]\leq[/tex] 921/64.
Therefore, the maximum height of the soccer ball is 921/64, or aprroximately 14.4(units)
"=" when 4t = 27/8, or t = 27/32.
The sum of the roots of a quadratic is 1 and the product of the roots is -35/4.
a. find the quadratic.
b. find the roots
If the sum of the roots of a quadratic equation is 1 and the product of the roots is -35/4 and the equation is [tex]4x^2-4x-35=0[/tex] and the roots are 3.5 and -2.5
If the quadratic equation is [tex]ax^2+bx+c=0[/tex]
The sum of the roots = [tex]-\frac{b}{a}[/tex]
The product of the roots = [tex]\frac{c}{a}[/tex]
Sum of the roots = 1 = [tex]-\frac{b}{a}[/tex]
Product of the roots = [tex]-\frac{35}{4}[/tex] = [tex]\frac{c}{a}[/tex]
If we assume a as 1, then the equation comes out to be:
[tex]x^2-x-\frac{35}{4} =0[/tex]
Multiply the equation by 4 to get a simplified equation:
[tex]4x^2-4x-35=0[/tex]
[tex]4x^2[/tex] - 14x + 10x - 35 = 0
2x (2x - 7) + 5 (2x - 7) = 0
(2x - 7)(2x + 5) = 0
x = 3.5 and -2.5
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You find an apartment which charges $925 a month rent. each year the rent increases by 6%.
The monthly rent for the apartment would be $1238.84 in the fifth year.
What is the monthly rent for an apartment that charges $925 initially and increases by 6% each year?The problem states that the monthly rent for an apartment is $925. To calculate the rent for the second year, we need to increase this amount by 6%.
To do this, we first need to calculate 6% of $925. We can do this by multiplying 0.06 (which is equivalent to 6%) by $925:
6% of $925 = 0.06 × $925 = $55.50
So, the rent for the second year would be:
$925 + $55.50 = $980.50
To find the rent for the third year, we need to increase the rent for the second year by 6%. We can follow the same process:
6% of $980.50 = 0.06 × $980.50 = $58.83
So, the rent for the third year would be:
$980.50 + $58.83 = $1039.33
To find the rent for any year n, we use the formula:
Rent for year n = $925 × (1 + 0.06)^n
In this formula, (1 + 0.06) represents the multiplier used to calculate the new rent each year.
For example, the multiplier for the second year is 1 + 0.06 = 1.06, and the multiplier for the third year is 1.06 × 1.06 = 1.1236 (rounded to four decimal places).
To find the rent for the fifth year, we plug in n = 5:
Rent for year 5 = $925 × (1 + 0.06)^5 = $925 × 1.3382 = $1238.84 (rounded to the nearest cent)
So, the monthly rent for the apartment would be $1238.84 in the fifth year.
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A group of 6 friends went to the movies. In addition to their tickets, they bought a large bag of popcorn to share for $9. 50. The total was $54. 50. Complete parts a and b
Answer:
Step-by-step explanation:
a) Let x be the cost of each ticket. Then the total cost of the tickets for the 6 friends is 6x. The total cost, including the popcorn, is $54.50. So we can set up an equation:
6x + $9.50 = $54.50
Solving for x, we get:
6x = $45.00
x = $7.50
So each ticket costs $7.50.
b) To find the cost per person, we need to add up the cost of each ticket and divide by the number of people. The cost of all 6 tickets is:
6 tickets × $7.50/ticket = $45.00
Adding the cost of the popcorn, we get:
$45.00 + $9.50 = $54.50
So the total cost for the 6 friends is $54.50, and the cost per person is:
$54.50 ÷ 6 people = $9.08 per person.
Therefore, each person contributed $9.08 towards the total cost of the tickets and popcorn.
Lily's age is 2 years and 4 months.
Hugo's age is 1 year and 8 months.
Write Lily's age in months as a fraction of Hugo's age in months.
Give your answer in it's simplest form.
Answer:
7/5
Step-by-step explanation:
Lily's age in months: 2×12+4=28mo
Hugo's age in months=12+8=20
Lily's age over Hugo's age: 28/20
Simplify:
28/20=14/10=7/5
Question 1 2 pts A researcher is interested in determining whether sugar consumption increases memory. She recruits 100 participants and randomly assigns them to one of two groups, sugar vs. No sugar. She then measures their word recall: Sugar group: M = 4. 5, SD = 1. 8, n = 55 • No sugar group: M = 2. 6, SD =. 68, n = 45 1. Is this an example of a quasi-experimental design? (yes or no) 2. What is the dependent variable? 3. What is the independent variable?
1. This is not an example of a quasi-experimental design because the researcher randomly assigned participants to the two groups. In a quasi-experimental design, the researcher does not have full control over the assignment of participants to groups.
2. The dependent variable in this study is the word recall. It is the variable that the researcher is interested in measuring and is expected to be affected by the independent variable.
3. The independent variable in this study is sugar consumption. It is the variable that the researcher manipulated by assigning participants to one of two groups, sugar vs. no sugar.
The purpose of manipulating the independent variable is to examine its effect on the dependent variable, word recall.
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Victoria has $200 of her birthday gift money saved at home, and the amount is modeled by the function h(x) = 200. She reads about a bank that has savings accounts that accrue interest according to the function s(x) = (1. 05)x−1. Explain how Victoria can combine the two functions to model the total amount of money she will have in her bank account as interest accrues after she deposits her $200. Justify your reasoning.
WILL GIVE BRANLIEST
The reasoning behind this is that the initial amount (h(x)) is multiplied by the interest growth factor (s(x)) to calculate the total amount with interest over time.
To model the total amount of money Victoria will have in her bank account as interest accrues after depositing her $200, you can combine the two functions h(x) and s(x). The given functions are h(x) = 200 and s(x) = (1.05)^x−1.
First, note that s(x) represents the growth factor of the interest, which is 5% (1.05) compounded annually. To find the total amount after x years, you need to multiply the initial amount by the growth factor raised to the power of x.
So, the combined function T(x) can be written as T(x) = h(x) * s(x).
Substitute the given functions into the combined function:
T(x) = (200) * ((1.05)^x−1)
This function, T(x), models the total amount of money Victoria will have in her bank account after x years with interest accrued on her $200 deposit. The reasoning behind this is that the initial amount (h(x)) is multiplied by the interest growth factor (s(x)) to calculate the total amount with interest over time.
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Josie had 12 beads on her necklace. Then she added b more beads. Write an expression that shows how many beads are on the necklace in all. please write a expression like b-12 or b+?
The expression that shows how many beads are on the necklace in all is:
b + 12.
What is expression?An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Expressions are often used to describe or represent real-world situations, and can be simplified, evaluated, or manipulated using algebraic rules and properties.
In the given question,
To write an expression that shows how many beads are on Josie's necklace in all after adding b more beads:
Start with the initial number of beads on the necklace, which is 12.
To this, add the number of beads Josie added, which is b.
Combine the two terms to form the final expression: 12 + b.
Therefore, the expression that shows how many beads are on Josie's necklace in all after adding b more beads is 12 + b.
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John owns 10 shirts and needs to select 5 to wear to school next week. How many ways can he choose the shirts? (hint: combinations)
50 ways
B 252 ways
500 ways
D 792 ways
There are 252 different combinations of shirts, the correct option is B.
In how many ways he can choose the shirts?Remember that if you have N elements, and you want to select K of these, the number of combinations is given by:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
Here we have 10 shirts and we want to select 5 of these, so the number of combinations is given by:
[tex]C(10, 5) = \frac{10!}{(10 - 5)!*5!} \\\\C(10, 5) = \frac{10*9*8*7*6}{5*4*3*2} = 252[/tex]
There are 252 different combinations, so the correct option is B.
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The vertices of a quadrilateral in the coordinate plane are known. How can the perimeter of the figure be found?
O Use the distance formula to find the length of each side, and then add the lengths.
Use the slope formula to find the slope of each of side, and then determine if the opposite sides are parallel.
O Use the slope formula to find the slope of each of side, and then determine if the consecutive sides are perpendicul
O Use the distance formula to find the length of the sides, and then multiply two of the side lengths.
Answer:..
Step-by-step explanation:Use the distance formula to find the length of each side and then add the lengths.
Use the slope formula to find the slope of each of side, and then determine if the opposite sides are parallel.
Use the slope formula to find the slope of each of side, and then determine if the consecutive sides are perpendicular.
Use the distance formula to find the length of the sides, and then multiply two of the side lengths.
Is these cosine or tangent or sine ? I need help with them can somebody tell me the answer to all three
Answer:
Step-by-step explanation:
I assume the question is what trig function do you use to find x? If that's correct then answers, from TOP to BOTTOM, are:
tan
cos
sin
Answer:
Triangle 1: tangent
Triangle 2: cosine
Triangle 3: sine
Step-by-step explanation:
First, some definitions before working the problem:
The three standard trigonometric functions, cosine, tangent, and sine, are defined as follows for right triangles:
[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]
[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]
[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]
One memorization tactic is "Soh Cah Toa" where the first capital letter represents one of those three trigonometric functions, and the "o" "a" and "h" represent the "opposite" "adjacent" and "hypotenuse" respectively.
The triangle must be a right triangle, or there wouldn't be a "hypotenuse", because the hypotenuse is always across from the right angle.
Triangle 1
For the first triangle, the known acute angle is in the bottom left. The two sides of the triangle that are known or are a "goal to find" are not the hypotenuse, so they are the "opposite" & "adjacent".
Specifically, the side of length "13" is touching the known acute angle AND the right angle, so it is the adjacent side. The unknown side of length "x" is is touching the right angle but is NOT touching the known acute angle, so it is the "opposite" (across from the angle).
Out of "Soh Cah Toa," the part that uses o & a is "Toa". The "T" in "Toa" stands for Tangent. So, the desired function to use for the first triangle is the Tangent function.
Triangle 2
For the second triangle, the known acute angle is in the top left. This time, the "adjacent" side is unknown, labeled as x, so it is the "goal to find" side. The "hypotenuse" is known.
Therefore, the two sides of the triangle that are known or are a "goal to find" are the "adjacent" & "hypotenuse".
Out of "Soh Cah Toa," the part that uses "a" & "h" is "Cah". So, the desired function to use for the first triangle is the Cosine function.
Triangle 3
For the third triangle, the known acute angle is in the top right.
This time, the side (at the bottom) across from the angle (at the top right) is known -- the "opposite" leg. Additionally, the "hypotenuse" is unknown and is our "goal to find" side.
Therefore, the two sides of the triangle that are known or are a "goal to find" are the "opposite" & "hypotenuse".
Out of "Soh Cah Toa," the part that uses "o" & "h" is "Soh". So, the desired function to use for the first triangle is the Sine function.
Greg, Harry and Ian share their electricity bill in the ratio 2:4:5.
how much dies each of them pay when their electricity bill are 1) 110$ 2) 165$ 3) 352$
pls answer quickly
The amount each of them pays when their electricity bill is $110, $165, and $352 respectively, in the ratio 2:4:5, are:
1) $20, $40, $50
2) $30, $60, $75
3) $64, $128, $160
1. How much do they pay for a $110 electricity bill?To find out how much each of them pays, we'll use the given ratio of 2:4:5 and divide the total bill among them accordingly.
Total bill: $110
The total ratio is 2+4+5=11.
Greg's share: (2/11) * $110 = $20
Harry's share: (4/11) * $110 = $40
Ian's share: (5/11) * $110 = $50
Therefore, Greg pays $20, Harry pays $40, and Ian pays $50.
2. How much do they pay for a $165 electricity bill?Total bill: $165
The total ratio is still 2+4+5=11.
Greg's share: (2/11) * $165 = $30
Harry's share: (4/11) * $165 = $60
Ian's share: (5/11) * $165 = $75
Therefore, Greg pays $30, Harry pays $60, and Ian pays $75.
3. How much do they pay for a $352 electricity bill?Total bill: $352
The total ratio remains the same: 2+4+5=11.
Greg's share: (2/11) * $352 = $64
Harry's share: (4/11) * $352 = $128
Ian's share: (5/11) * $352 = $160
Therefore, Greg pays $64, Harry pays $128, and Ian pays $160.
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A cuboid is placed on top of a cube, as shown in the diagram, to form a solid.
2 cm
3 cm
The cube has edges of length 7 cm.
The cuboid has dimensions 2 cm by 3 cm by 5 cm.
Work out the total surface area of the solid.
Optional working
Ansv
cm²
+
5 cm
7 cm
Answer: 344cm²
Step-by-step explanation:
7x7=49
49x5=245
3x2=6
49-6=43
245+43=288
5x2=10 10x2=20
5x3=15 15x2=30
288+30+20+6=344
The number of revolutions
made by a tire traveling over a fixed distance
varies inversely with the radius of the tire. a
12-inch radius tire makes 100 revolutions to
travel a certain distance. how many
revolutions would a 16-inch radius tire require
a
to travel the same distance?
define variables
identify constant of variation
write an equation and show work (please can someone help with this stuff, my deadline is in 4 days)
A 16-inch radius tire would require 75 revolutions to travel the same distance as a 12-inch radius tire that made 100 revolutions.
Let's start by defining some variables. Let "r" represent the radius of the tire and "n" represent the number of revolutions it makes over a fixed distance. We are given that the number of revolutions is inversely proportional to the radius of the tire. This means that as the radius increases, the number of revolutions decreases, and vice versa. We can express this relationship mathematically as follows:
n = k/r
Here, "k" is the constant of variation, which remains the same for any given tire traveling over the same distance. To solve the problem, we need to find the value of "k" first. We know that a 12-inch radius tire makes 100 revolutions to travel a certain distance. Substituting these values into the equation, we get:
100 = k/12
Solving for "k," we get k = 1200. Now we can use this value to find the number of revolutions required by a 16-inch radius tire to travel the same distance:
n = 1200/16 = 75
Therefore, a 16-inch radius tire would require 75 revolutions to travel the same distance as a 12-inch radius tire that made 100 revolutions.
In summary, we defined the variables, identified the constant of variation, wrote the equation (n=k/r), found the value of the constant by using the given information, and used it to solve the problem by finding the number of revolutions required by a tire with a different radius.
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In the year 2001, a company made $7. 2 million in profit. For each consecutive year after that, their profit increased by 11%. How much would the company's profit be in the year 2005, to the nearest tenth of a million dollars?
The company's profit in the year 2005 would be approximately $10.5 million.
Let's calculate the company's profit for the year 2005 using the given information.
Initial profit in 2001: $7.2 million
Annual profit increase: 11%
We need to find the profit for 2005, which is 4 years after 2001.
Step 1: Identify the formula for compound interest, which can be applied to profit increase:
Future Profit = Initial Profit * (1 + Profit Increase Rate)^Number of Years
Step 2: Plug in the values:
Future Profit [tex]= $7.2 million * (1.11)^4[/tex]
Step 3: Calculate the result:
Future Profit [tex]= $7.2 million * (1.11)^4[/tex]
Future Profit = $7.2 million [tex]* 1.4641[/tex]
Future Profit = $10.54152 million
Step 4: Round the result to the nearest tenth of a million dollars:
Future Profit ≈ $10.5 million
So, the company's profit in the year 2005 would be approximately $10.5 million.
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An office manager orders one calculator or one calendar for each of the office's 80 employees. Each calculator costs $12, and each calendar costs $10. The entire order totaled $900.
Part A: Write the system of equations that models this scenario.
Part B: Use substitution method or elimination method to determine the number of calculators and calendars ordered. Show all necessary steps.
The system of equations is.
x + y = 80
12x + 10y = 900
And the solutions are y = 30 and x = 50
How to write and solve the system of equations?Let's define the two variables:
x = number of calculators.
y = number of calendars.
With the given information we can write two equations, then the system will be:
x + y = 80
12x + 10y = 900
Now let's solve it.
We can isolate x on the first equation to get:
x = 80 - y
Replace that in the other equation to get:
12*(80 - y) + 10y = 900
-2y = 900 - 960
-2y = -60
y = -60/-2 = 30
Then x = 50
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stressing outtt I need help its due in a few minuets
What is the length of the segment indicated by the question mark
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{6.6+x}\\ a=\stackrel{adjacent}{6.6}\\ o=\stackrel{opposite}{8.8} \end{cases} \\\\\\ (6.6+x)^2= (6.6)^2 + (8.8)^2\implies (6.6+x)^2=121\implies (6.6+x)^2=11^2 \\\\\\ 6.6+x=11\implies x=4.4[/tex]
Write a function to model the volume of a rectangular prism if the length is 26cm and the sum of the width and height is 32cm. what is the maximum possible volume of the prism?
To model the volume of a rectangular prism with length 26cm and width w and height h such that the sum of the width and height is 32cm, we can use the following function:
V(w, h) = 26wh
subject to the constraint:
w + h = 32
We can solve for one of the variables in the constraint equation and substitute it into the volume equation, giving us:
w + h = 32 => h = 32 - w
V(w) = 26w(32 - w) = 832w - 26w^2
To find the maximum possible volume, we can take the derivative of this function with respect to w and set it equal to zero
dv/dw= 832 - 52w = 0
Solving for w, we get:
w = 16
Substituting this value back into the constraint equation, we get:
h = 32 - w = 16
Therefore, the maximum possible volume of the prism is:
V(16, 16) = 26(16)(16) = 6656 cubic cm
So the function to model the volume of the rectangular prism is V(w) = 832w - 26w^2, and the maximum possible volume is 6656 cubic cm when the width and height are both 16cm.
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Determine the location and value of the absolute extreme values off on the given interval, if they exist 8x? f(x) - +22x2 - 24x on (-7,11 G What in are the absolute maximum maxime off on the given interval? Select the correct choice below and, if necessary, to in the answer bowen to completo your choice A. Tho absolute maximum/maxima isarea- (Use a comma to separato answers as needed. Type exact answers, using radicals as rended) B. There is no absolute maximum off on the given interval What are the absolute minimum/minima off on the given interval? Select the correct choice below and. If necessary, in the wwer boxes to complete your in O A The absolute minimum/minima is/are at (Use a comma to separate answers as needed. Type exact answers, using radical as needed) B. There is no absolute minimum off on the given interval
The absolute maximum will be at (11, 10373).
The absolute minimum is at (-1.963, -25.294).
What in are the absolute maximum maxime off on the given interval?
To determine the location and value of the absolute extreme values of the function f(x) = 8x³+ 22x² - 24x on the interval (-7, 11), follow these steps:
Find the critical points by taking the derivative of the function and setting it equal to zero:
f'(x) = 24x² + 44x - 24
Solve for x:
Factor the equation: 4(6x² + 11x - 6) = 0
Using the quadratic formula, x = (-11 ± √(121 + 144))/12
x ≈ -1.963, 0.630
Check the endpoints and the critical points to find the absolute maximum and minimum:
f(-7) ≈ 461
f(-1.963) ≈ -25.294
f(0.630) ≈ -16.102
f(11) ≈ 10373
Compare the values:
The absolute maximum is at x = 11, with a value of 10373.
The absolute minimum is at x ≈ -1.963, with a value of ≈ -25.294.
Answer:
The absolute maximum is at (11, 10373).
The absolute minimum is at (-1.963, -25.294).
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What is the mean of the data set fifth grade jump distance
The mean of the fifth-grade jump distance data set.
How to calculate the mean of fifth-grade jump distances?To determine the mean of the data set for fifth-grade jump distances, we need the actual data values. Without the specific data set, it is not possible to calculate the mean.
The mean is the sum of all the values in a data set divided by the number of values. Therefore, we would need the individual jump distances for each fifth-grade student to calculate the mean accurately.
Once we have the complete data set, we can add up all the distances and divide by the total number of students to find the mean. Without the specific data, we cannot provide a numerical answer for the mean of the fifth-grade jump distance.
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Analyze the diagram below and answer the questions that follow.
F
G
t
How many different ways can the line above be named? What are those names?
A. 2 ways; FG, GF
B. 3 ways; t, FG, GF
C. 4 ways; t, FG, FG, GF
D. 5 ways; t, FG, GF, FG GF
Answer: A. 2 ways; FG, GF
Step-by-step explanation: There are only two ways to name a line, and they are interchangeable: starting from one endpoint and naming the other endpoint second, or starting from the second endpoint and naming the first endpoint second.
A cake is in the shape of a rectangular prism. It has a length of 13 inches, a width of 8 inches, and a height
of 5 inches. A baker will put frosting on all sides of the cake except for the bottom. What is the total surface area
of the cake that will be covered in frosting?
Show Your Work
O 114 in.
0 334 in.
O 449 in?
O 573 in?
If the cake is in the shape of a rectangular prism, the total surface area of the cake that will be covered in frosting is 314 sq. inches.
To find the total surface area of the cake that will be covered in frosting, we need to calculate the area of all sides except the bottom. A rectangular prism has 6 sides, and we will be considering 5 of them.
Surface area of top: length × width = 13 × 8 = 104 sq. inches
Surface area of front: length × height = 13 × 5 = 65 sq. inches
Surface area of back: length × height = 13 × 5 = 65 sq. inches
Surface area of left side: width × height = 8 × 5 = 40 sq. inches
Surface area of right side: width × height = 8 × 5 = 40 sq. inches
Now, we will sum the areas of all these sides:
104 + 65 + 65 + 40 + 40 = 314 sq. inches
So, the total surface area of the cake that will be covered in frosting is 314 sq. inches. None of the provided options match this answer, so it is important to double-check the question for any discrepancies.
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Ying Yu bought a rectangular box to display her doll collection. She decided
to exchange the box for a similar one that had five times its dimensions.
How does the volume of the larger rectangular box compare to the volume
of the smaller box?
The volume of the larger rectangular box is 125 times the volume of the smaller box.
To compare the volume of the larger rectangular box to the smaller box, we need to consider how the dimensions have changed.
Since the larger box has dimensions 5 times those of the smaller box, let's represent the dimensions of the smaller box as length (L), width (W), and height (H). Therefore, the dimensions of the larger box would be 5L, 5W, and 5H.
Now, let's calculate the volume of both boxes:
1. Volume of the smaller box: V_small = L * W * H
2. Volume of the larger box: V_large = (5L) * (5W) * (5H)
To find the ratio of the larger box's volume to the smaller box's volume, we can divide the volumes:
V_large / V_small = ((5L)*(5W)*(5H)) / (L * W * H)
Notice that L, W, and H can be canceled out:
(5 * 5 * 5) = 125
So, the volume of the larger rectangular box is 125 times the volume of the smaller box.
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11. The spread of a drop of food dye throughout a glass of milk is called__________
Answer: Diffusion
Step-by-step explanation: