we get that the volume of each object is
[tex]\begin{gathered} V_{\text{box}}=13^3=2197 \\ V_{\text{ball}}=\frac{4}{3}\cdot\pi\cdot(5.5)^3\approx696.90997032\approx697 \end{gathered}[/tex]so the reamining space is:
[tex]2197-697=1500[/tex]f(x) = -x² + 8x - 12; Find ƒ(3)
The result of the function f(3) is 3.
What does it mean to evaluate function?The process of evaluating a function is typically straightforward when we have the function in the form of a formula. When a function is evaluated, a variable is replaced with its provided value or expression. Example. For x = 5, evaluate f(x) = 2x + 4. This implies to simplify and change x to 5. It is advised to enclose the value being substituted in parentheses.Given:
f(x) = -x² + 8x - 12
x = 3
Putting the value of x in the given function to obtain the outcome of the function,
f(3) = -(3)² + 8 × 3 - 12
= -9 + 24 - 12
= 24 - 21
= 3
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Solve. 5(y - 10) = -5 Answer: Submit Answer att
We divide both sides by 5 so we can eliminate the parenthesis:
[tex]\begin{gathered} 5(y-10)=-5 \\ \frac{5(y-10)}{5}=-\frac{5}{5} \\ y-10=-1 \end{gathered}[/tex]Step 2We rearrange the terms so the terms with the unkown variable y are on the left side and the other ones on the right side:
y - 10 = -1
↓ adding 10 both sides
y - 10 + 10 = -1 + 10
y + 0 = 9
y = 9
Answer: y = 9A department store is having an after-Christmas sale in which
coats are discounted 30% and suits are discounted 25. If Joe
purchases a coat that was originally $300 and a sair that was
originally $400, how much money did he spend
In total, he spend $510 after discount.
What is discount?A deduction taken from the gross amount or worth of anything, such as a price decrease made from the standard or list price, giving clients a 10% discount to purchase tickets. A proportionate withdrawal from a loan account, typically done in exchange for cash or quick payment.
Given Data
Coats are discounted 30%
Suits are discounted 25%
Joe purchased a coat of $300
= 300 - [tex]\frac{30}{100}[/tex] × 300
= 300 - 90
= 210
He purchased coat for $210.
He purchased a suit $400.
Suits are discounted 25%
= 400 - [tex]\frac{25}{100}[/tex] × 400
= 400 - 100
= 300
He purchased suit for $300.
In total, he spend $510 after discount.
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Kaj earns $35 for 2 hours of work. If she makes a constant hourly wage, which table
represents the relationship between the number of hours she works and her total
earnings?
The table of values of the relationship between time and earnings is a linear relation
How to determine the table of values that represents the earnings?From the question, we have the following parameters:
Number of hours = 2 hours
Total earnings in this time = $35
Also from the question, we understand that:
She makes a constant hourly wage
A constant hourly wage implies that the table of values has a linear relationship
In this case, the linear relationship is represented as
A(t) = constant hourly wage * t
Where
A(t) represents the earnings
t represents the number of hours
So, we have
constant hourly wage * 2 = 35
Divide both sides of the equation by 2
So, we have
constant hourly wage = 17.5
Substitute constant hourly wage = 17.5 in A(t) = constant hourly wage * t
A(t) = 17.5 * t
Evaluate
A(t) = 17.5t
Using the values of t as:
t = 0, 2, 4, 6
We have the following table of values
Number of hours (t) || Amount earned
0 0
2 35
4 70
6 105
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how many 14 goes into 78
The amount of times that 14 goes into 78 is; 5 times
How to carry out division of numbers?
We want to find how many 14 goes into 78.
Now, it is pertinent to note that this expression is used in our common daily lives for basic things of life. For example, if i want to know how many 10 dollars can go into 100 dollars, i will just divide 100 by 10.
Similarly another example is if i want to know how many 5 liters container of fuel would go into a 60 liters tank, i will just divide 60 by 5 to get the number.
In a similar vein, we can solve this question by dividing 78 by 14 to get;
78/14 = 5 ⁸/₁₄
This means 14 can only go in 5 full times as we will not count the fraction.
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Only question #15,17, and 19 please show work THANK YOU
15) Magnitude of projection is 6.325
17) Projection is <-3.6, 10.8>
19) The acute angle between and vector is 34.509°.
The magnitude of the projection of A vector onto B vector could be deduced as,
Proj V(a) ÷ V(b) = (V(a) · V(b)) ÷ |V(b)|
15) Given, coordinates <8,-4> and <1,-3>
|V(b)| = √((1)² + (-3)²)
|V(b)| = √(1+9)
|V(b)| = √10
Proj V(a) ÷ V(b) = (V(a) · V(b)) ÷ |V(b)|
Proj V(a) ÷ V(b) = (8, -4) · (1, -3) ÷ √10
Proj V(a) ÷ V(b) = (8 + 12) ÷ √10
Proj V(a) ÷ V(b) = 20 ÷ √10
Proj V(a) ÷ V(b) = 2√10 = 6.325
17) Given, coordinates <-6,10> and <1,-3>
Projection = Proj V(a) ÷ V(b) = ((V(a) · V(b)) ÷ |V(b)|) × <1, -3>
|V(b)| = √((1)² + (-3)²)
|V(b)| = √(1+9)
|V(b)| = √10
Proj V(a) ÷ V(b) = (V(a) · V(b)) ÷ |V(b)| × <1, -3>
Proj V(a) ÷ V(b) = ((-6, 10) + (1, (-3)) ÷ √10) × <1, -3>
Proj V(a) ÷ V(b) = ((-6 × 1) + (10 × (-3)²) ÷ √10) × <1, -3>
Proj V(a) ÷ V(b) = ((-6 + 90) ÷ √10) × <1, -3>
Proj V(a) ÷ V(b) = ((84) ÷ √5) × <1, -3>
Proj V(a) ÷ V(b) = <-3.6, 10.8>
19) The vector are <2,3> and <-5,-2>. The acute angle between and vector is 34.509°.
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In a poll, 1,004 men in a country were asked whether they favor or oppose the use of "federal tax dollars to fund medical research using stem cells obtained from human embryos." Among the respondents, 48% said that they were in favor. Identify the population and the sample.
Question content area bottom
All adults in the country and considered as population. 1003 men in the country are adults that are selected.
What is sample?Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.
Given Data
In a poll, 1,004 men in a country were asked whether they favor or oppose the use of "federal tax dollars to fund medical research using stem cells obtained from human embryos." Among the respondents, 48% said that they were in favor.
1)Population
All adults in the country and considered as population.
2) Sample is
1003 men in the country are adults that are selected.
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Does the table show a proportional relationship? If so, what is the value of y when x is 11?
x 4 5 6 10
y 64 125 216 1,000
Need an explanation to this equation? Radius how do I find it?
Solution
[tex]x^2-10x+y^2+6y-30=0[/tex]Now, the circle equation
[tex]\left(x−a\right)^2+\left(y−b\right)^2=r^2\:\:\mathrm{is\:the\:circle\:equation\:with\:a\:radius\:r,\:centered\:at}\:\left(a,\:b\right)[/tex][tex]undefined[/tex]Rewrite in standard form
[tex]\left(x-5\right)^2+\left(y-\left(-3\right)\right)^2=8^2[/tex]Therefore the circle properties
[tex]\left(a,\:b\right)=\left(5,\:-3\right),\:r=8[/tex]The final answer
[tex]\mathrm{Circle\:with\:center\:at}\:\left(5,\:-3\right)\:\mathrm{and\:radius}\:r=8[/tex]Each letter is three. 5 m away from the base of the building. How high is window A?
Solution
A
Using pythagorean theorem
[tex]\begin{gathered} 5.5^2=3.5^2+A^2 \\ 30.25=12.25+A^2 \\ Re-arrange \\ A^2=30.25-12.25 \\ A^2=18 \\ Take\text{ the square root of both sides} \\ A=\sqrt{18} \\ A=4.2426 \end{gathered}[/tex]The final answer
The height of window A is
[tex]4.24meters[/tex]
What is the value of 2x + 11y when x = 4 and y = 2? 303848136
We want to find the value of the expression;
[tex]2x+11y[/tex]When x = 4 and y = 2.
All we have to do is substitute these values; when we do that, we have;
[tex]\begin{gathered} 2(4)+11(2) \\ =8+22 \\ =30 \end{gathered}[/tex]Therefore, the answer is 30.
What is 50% of 100%?
Answer:
We need to determine 50% of 100 now and the procedure explaining it as such
Step 1: In the given case Output Value is 100.
Step 2: Let us consider the unknown value as x.
Step 3: Consider the output value of 100 = 100%.
Step 4: In the Same way, x = 50%.
Step 5: On dividing the pair of simple equations we got the equation as under
100 = 100% (1).
x = 50% (2).
(100%)/(x%) = 100/50
Step 6: Reciprocal of both the sides results in the following equation
x%/100% = 50/100
Step 7: Simplifying the above obtained equation further will tell what is 50% of 100
x = 50%
Therefore, 50% of 100 is 50
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Help on math problem precalculus
Remember that the domain is the numbers that x can take
x=5 has a domain of only 5
y = 1/x cannot have a value of x=0 because 1/0 is undefined
t = sqrt(x) cannot have negative values because sqrt( negative numbers) is not defined in the real number system
y = |x| is defined for all values of x so it has a domain of all real numbers
PLEASE ANSWER QUICK ILL GIVE BRAINLIEST IF CORRECT
Answer:
domain: [-1,4]
range: [-2,4]
the graph is not a function, this is proven by using the vertical line test.
hope this helps :)
1. A triangle is rotated 90° about the origin. What is true about the relationship between the image and the
pre-image?
(1 point)
The lengths of the sides and the measures of the angles are preserved, so the triangles are congruent.
The lengths of the sides are enlarged and measures of the angles are preserved, so the triangles are similar.
The lengths of the sides change and the measures of the angles change as well, so the triangles look nothing alike.
The lengths of the sides are reduced and measures of the angles are preserved, so one triangle is a reduction of the other.
Answer:
the first answer option : all lengths and angles stay the same.
Step-by-step explanation:
imagine you have a piece of plastic or glass of a triangular shape on your table.
now, lower your hand on the table, so that your thumb touches the table and one of your other fingers touches the triangle on the top.
and now twist your hand that your thumb stays at the same point, and your finger holding the triangle starts making a circular motion.
that finger is dragging the triangle along.
what happens to the triangle ? it keeps its original shape, and changes only its location and orientation.
that is what a rotation is.
x ÷ 5 - 13 = 2
What is x?
Answer:
75
Step-by-step explanation:
Answer:
75. ..... ............................
A college professor hands out a list of 16 questions, 8 of which will appear on the final examination for the course. One of the students taking the course is pressed for time and can prepare for only 9 of the 16 questions on the list. Suppose the professor chooses the 8 questions at random from the 16. What is the probability that the student will be prepared for exactly 4 questions?
The probability that the student will be prepared for exactly 4 questions is; 0.3427
How to solve Hypergeometric Probability distribution?
Hypergeometric distribution is defined as a discrete probability distribution that expresses the probability of k successes in n draws, done without replacement, from a finite population of size N that contains exactly K objects with that feature. In this disdtribution, each draw is either a success or a failure.
The probability mass function of Hypergeometric distribution is given by the formula;
P(K = k) = KCk * N-KCn-k ]/NCn
Now, the probability that the student will be prepared for exactly 4 questions will be;
P(K = 4) where;
N = 16
K = 9
n = 8
Solving P(K = 4) = 9C4* 16-9C8-4 ]/16C8 = 0.3427
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In a class there are
10 students who play football and cricket
7 students who do not play football or cricket
14 students who play football
21 students who play cricket
Find the probability that a student chosen at random plays football and cricket.
Answer: 31.25%
Step-by-step explanation:
Draw a Ven diagram in a rectangle with 2 circles one for F and the other for C. The intersection overlap will have the 10 who play both outside the circles but within the rectangle the 7 who do neither so then fill the rest of F with 4 to give a total of 14 and 11 for the C to total 21. When you add all the numbers you’ll get a class total of 32. Then the % who play both F and C is = (10/32)*100 = 31.25%
solve the system of equations using the elimation menthod. show your work. make sure to express your solution as an ordered pair
-3x - 4y = -5
12x - 3y = -18
Multiply the first equation by 4, and add both
-12x - 16y = -20
+
12x - 3y = -18
___________
-19y = -38
Solve for y:
y = -38/-19
y= 2
Replace y on any equation and solve for x
-3x - 4(2)=-5
-3x -8 = -5
-3x = -5+8
-3x = 3
x=3/-3
x=-1
Solution = (-1,2)
If x=8, y=4 z=2 then what is 3z(x-z)-y(x/2)
Tavon has a gift card for $175 that loses $4 for each 30-day period it is not used. He has another gift card for $155 that loses $3.50 for each 30-day period it is not used. a. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal. b. What will the value of each card be when they have equal value? a. If x is the number of 30-day periods, then the equation can be used to find the number of 30-day periods until the values of the gift cards will be equal. (Type an equation. Use integers or decimals for any numbers in the equation.)
Answer:
A) 40
B) $ 15
Step-by-step explanation:
A)An equation for the number of 30-day periods until the value of the gift cards will be equal
Let x be the number of time periods for which the gift card is not used, then
For the gift card $ 155 if it is not used for x periods, then the amount that will be lost is
155 - 3.50 x---------------------(1)
For the gift card $ 135 if it is not used for x periods, then the amount that will be lost is
135 - 3x---------------------- (2)
Now when both the amount lost is equal
solving the equation, we get
20 = 0.5x
x = 40Thus the value of gift cards will be equal for 40 ,30 day periods. B)The value of each card be when they have equal value The two cards will have equal value after 40 30 day periods, this denotes that at this time, the value of each card will be equal.Then substituting x = 40, we get when they have equal value, the value of each card will be $15
Use basic facts and patterns to find 30x30
Answer: Well, 10 x 3, 10 x 3
Step-by-step explanation: I think thats what you are asking?
Amy is experimenting with three different strawberry smoothie recipes. She makes all three smoothies for each of her x friends. The first recipe uses 4 strawberries per smoothie, the second recipe uses 5, and the third recipe uses 6. Pick all the expressions that represent how many strawberries Amy needs for all the smoothies.
The total number of strawberries needed for making all the smoothies can be represented by the expression -
y = 15x
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is Amy who is making all three smoothies for each of her x number friends. The first recipe uses 4 strawberries per smoothie, the second recipe uses 5, and the third recipe uses 6.
Number of friends [n] = x
Each of the three friends will get smoothies made from recipe 1, recipe 2 and recipe 3.
Then -
Number of strawberries needed for smoothie made from recipe 1 for x friends = n[1] = 4x
Similarly, for smoothies made from recipe 2 and 3 will need -
n[2] = 5x and n[3] = 6x number of strawberries.
Assume that total number of strawberries needed for making all the smoothies are y. Then, we can write -
y = 4x + 5x + 6x
y = 15x
Therefore, the total number of strawberries needed for making all the smoothies can be represented by the expression -
y = 15x
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According to a recent survey, the number of pet dogs and cats in
the United States is about 183,900,000. Write an estimate for the number of pet dogs and cats as a single digit times an integer
power of 10. Show your work.
An estimate for the number of pet dogs and cats in the United States based on a recent survey, written as a single digit times an integer power of 10 is 2 x 10⁸.
What is an estimate?An estimate is a rough calculation or judgment arrived at when the details are not required or available.
We can apply number approximation, rounding, and scientific notations in estimation, as above.
First, the number, 183,900,000, can be approximated to 200 million pet dogs as an estimate.
Then, 200,000,000 can be written in a standard form or scientific notation by using an integer that indicates the place value in the power of 10.
Thus, 183,900,000 pet dogs can be estimated as 2 x 10⁸.
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The original price of a DVD is $12 the sale Price is 35% of the original price final total cost of the DVD
Answer: $4.20
Step-by-step explanation:
The sale price is $12 * .35 = 4.2
The actual lengths of Wall A, Wall B, and Wall D are 2.5 m, 2.75 m, and 3.75 m. If 1 m = 4 cm then determine how long these walls will be on Noah’s scale drawing. Be sure to include your units; use 'cm' for centimeters.
Step-by-step explanation:
1 m = 4 cm
therefore,
A = 2.5 m = 2.5×1 m = 2.5×4 cm = 10 cm
B = 2.75 m = 2.75×1 m = 2.75×4 cm = 11 cm
D = 3.75 m = 3.75×1 m = 3.75×4 cm = 15 cm
Jean is trying to prove parallelogram LMNO is a rhombus by using coordinate geometry.
Which statement must be true to prove LMNO is a rhombus?
A) (slope of line MO)(slope of line LN) = -1
B) (slope of line MO)(slope of line LN) = 1
C) the midpoint of line MO is the midpoint of line LN
D) the distance from M to O = the distance from L to N
Answer:
D
Step-by-step explanation:
A and B don't prove anything because we have the slopes of sides LM and ON to worry about. C could mean that yes, the figure is a quadrilateral, but with those parameters it could be a square, a rectangle, or trapezoid. Therefore D is the correct answer
Diagonal Mo bisects diagonal LN.
Midpoint of line MO = Midpoint of line LN
Option C is the correct answer.
What is a parallelogram?Parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
In a rhombus,
- All sides are equal
- Opposite sides are parallel
- Diagonals bisect each other
- opposite angles are equal
Now,
Midpoint of line MO = Midpoint of line LN
Since diagonals bisect each other
Thus,
Diagonal Mo bisects diagonal LN.
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State the postulatr ir theorem for no. 6 and 9
Solution
Number 6
for this case we can see that we have two common angles and one equal side. By the way we have also a common side and then since we have right triangles the correct postulate would be:
SSS
Number 9
Needing help for this
The pairs of angles that are linear pairs involving point F are:
A. ∠DFC and ∠CFG
D. ∠HFD and ∠CFD
E. ∠GFH and ∠GFC
F. ∠HFG and ∠DFH
What is a Linear Pair?When two angles that are adjacent to each other, (that is, they share the same vertex and the same side), are located on a straight line, these angles are linear pairs and are also supplementary angles.
Making reference to the image given, angles DFC and CFG share a common vertex F and a common side CF. Also, they lie on a straight line. Therefore, angle DFC and angle CFG are a linear pair.
Angles HFD and CFD share a common vertex F and a common side FD. They lie on a straight line. Thus, angle HFD and angle CFD are also a linear pair.
The same thing applies to angle GFH and angle GFC, as well as angle HFG and angle DFH.
The linear pairs are:
A. angle DFC and angle CFG
D. angle HFD and angle CFD
E. angle GFH and angle GFC
F. angle HFG and angle DFH
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I need help with this one
Translation: add or subtract to the coordinates x ,y
A = (3,2)
A'= (6,-2)
(3+3, 2-4 ) = (6,2)
Solution:
(x,y) (x+3,y-4)→