1. 3/5x -7 = 23
A. x = 40
B. x = 45
C. x = 50
D. x = 55
2.When Patrick and Cameron went bowling at Victory Lanes, they spent a total of $42. This included rental of shoes at $3.50 per pair. Patrick bowled 2 games, and Cameron bowled 3 games.
How much did each game cost?
A. $6.00
B. $7.00
C. $7.70
D. $8.75
3.A local movie theater offers a special deal for birthday parties. The price, which covers the cost of the tickets and a box lunch, includes a flat fee of $75 plus $5 per ticket. Sarah’s parents spent $150 altogether at the theater to celebrate her birthday.
Which equation can be used to determine how many children, x, were in the group?
A. 75/150=5x
B. 150/75=5x
C. 150 = 5x – 75
D. 150 = 5x + 75
4. 35 + 0.25x = 53.75
A. x = 75
B. x = 140
C. x = 215
D. x = 250
5.T he perimeter of this isosceles triangle is 47 cm.
top point. (B) left bottom point (A) right bottom point (C) in between 12cm
What is the length of each of its legs (it doesn't have legs)?
A. 15 cm
B. 17.5 cm
C. 19.5 cm
D. 35 cm
Answers
3/5x = 23 + 7
3/5x = 30
x = 30/(3/5)
x = 30 * 5/3
x = 150/3
x = 50 <==
=====================
3.50(2) + 5g = 42
7 + 5g = 42
5g = 42 - 7
5g = 35
g = 35/5
g = 7 <== each game costs $ 7
===================
150 = 5x + 75
===================
35 + 0.25x = 53.75
0.25x = 53.75 - 35
0.25x = 18.75
x = 18.75 / 0.25
x = 75 <===
===================
if one leg is 12.....and an isosceles triangle has 2 equal sides....(47 - 12) / 2 = 35/2 = 17.5 <==
Related Questions
what is absolute value of these set of numbers?
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= -12 - 12 = -24
that's the determinant tho, not absolute value
A round pizza, with a 12.0 in diameter, is cut into 8 pie shaped pieces. What is the area of each slice (sector) of pizza?
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How do you write .625 as a fraction
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To turn a decimal into a fraction, first notice that the number to the right of the decimal point is 625. The 6 represents the tens, the 2 represents the hundreds, and the 5 represents the thousands. So, we can put 625 over 1000 or 625/1000.
Notice that the fraction [tex]\frac{625}{1000}[/tex] is not in lowest terms. To turn the fraction into lowest terms, we can divide both the numerator and the denominator by 125.
[tex]\frac{625}{1000}[/tex] ÷ [tex]\frac{125}{125}[/tex] = [tex]\frac{5}{8}[/tex]
Therefore, .625 can be written as the fraction 5/8, which is in lowest terms.
A bag contains 90 marbles some red and some transparent the ratio of red marbles to transparent ones is 1:4. how many red marbles are there? andwer
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You are building a new house on a cartesian plane whose units are measured in miles. Your house is to be located at the point (2,0) . Unfortunately, the existing gas line follows the curve y= √(16 x^2 +5x+16). It costs 400 dollars per mile to install new pipe connecting your house to the existing line. What is the least amount of money you could pay to get hooked up to the system?
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ANYONE????
Use infinite geometric summation to write 0.18 as a fraction whose numerator and denominator have no common factors. Recall that 0.18 means 0.18181818 . . . .
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The fracture toughness (in ) of a particular steel alloy is known to be normally distributed with a mean of 28.3 and a standard deviation of 0.77. We select one sample of this alloy at random and measure its fracture toughness. Given that the fracture toughness is at least 27, what is the probability that the fracture toughness will be between 29 and 40.3? is it just P(X <= 40.3) - P(X <= 29)? How do I use the 27?
Answers
The conditional probability is given as follows: The probability of an event A given B is given by
[tex]P(A|B)= \frac{P(A\cap B)}{P(B)} [/tex]
Thus, given that the fracture toughness of a particular steel alloy is known to be normally distributed with a mean of 28.3 and a standard deviation of 0.77.
The probability that the fracture toughness will be between 29 and 40.3 given that the fracture toughness is at least 27 is given by
[tex]P(29 \leq X \leq 40.3 \, | \, X \geq 27)= \frac{P(29 \leq X \leq 40.3)\cap P(X \geq 27)}{P(X \geq 27)} \\ \\ =\frac{P(29 \leq X \leq 40.3)}{P(X \geq 27)}[/tex]
[tex]P(29 \leq X \leq 40.3)=P\left(z \ \textless \ \frac{40.3-28.3}{0.77}\right)- P\left(z \ \textless \ \frac{29-28.3}{0.77}\right) \\ \\ =P(z\ \textless \ 15.58)-P(z\ \textless \ 0.91)=1-0.81835=0.18165[/tex]
[tex]P(X \geq 27)=1-P(x\ \textless \ 27) \\ \\ =1-P\left(z\ \textless \ \frac{27-28.3}{0.77}\right)=1-P(z\ \textless \ -1.688) \\ \\ =1-0.04568=0.95432[/tex]
Thus, the probability that the fracture toughness will be between 29 and 40.3 given that the fracture toughness is at least 27 is given by
[tex]\frac{P(29 \leq X \leq 40.3)}{P(X \geq 27)}= \frac{0.18165}{0.95432} =\bold{0.1903}[/tex]
What is the slope of y=1/5x - 4?
Answers
the slope is [tex] \frac{1}{5}[/tex] and the -4 is the intercept or where the line crosses the y- axis
5y-x=10 (solve for y).
Answers
To solve 5y - x = 10 for y, add x to both sides and then divide by 5, resulting in the solution y = (x + 10) / 5.
To solve the equation 5y - x = 10 for y, follow these steps:
Add x to both sides of the equation to isolate terms with y on one side: 5y = x + 10.
Now, divide both sides of the equation by 5 to solve for y:
y = (x + 10) / 5.
The solution for y when given an equation of the form 5y - x = 10 is y = (x + 10) / 5.
Sebastian made the following model to find the product of 17X24
Is his model correct? Expalin
Answers
17x24= 408
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The expression 1/3b−1/3 factored is
Answers
Answer:
[tex]\frac{1}{3}[b-1][/tex]
Step-by-step explanation:
we have
[tex]\frac{1}{3}b-\frac{1}{3}[/tex]
Factor the coefficient [tex]\frac{1}{3}[/tex] of both terms
[tex]\frac{1}{3}b-\frac{1}{3}=\frac{1}{3}[b-1][/tex]
by which conversion factor can 800 meters be multiplied to change in to miles?
Answers
and there are 1.609 kilometers in 1 mile.
if there are 1.609 kilometers in 1 mile, then there are 1.609 * 1000 meters in 1 mile, or 1609 meters
[tex]\bf \cfrac{800~\underline{m}}{1}\cdot \cfrac{mile}{1609~\underline{m}}\implies \cfrac{800}{1609}~mile\implies 800\cdot \cfrac{1}{1609}~mile[/tex]
What is the quotient?
-5 1/4 ÷ 2 3/4
Enter your answer as a mixed number, in simplified form, in the box.
Answers
= - 21/4 ÷ 11/4
= - 21/4 * 4/11
= - 21/11
= - 1 10/11
To divide -5 1/4 by 2 3/4, convert both numbers to improper fractions, multiply the first fraction by the reciprocal of the second fraction, and simplify the result. The quotient is -1 10/11.
Explanation:To divide -5 1/4 by 2 3/4, first convert both mixed numbers to improper fractions. -5 1/4 can be written as -21/4, and 2 3/4 can be written as 11/4. Next, divide -21/4 by 11/4. To divide fractions, multiply the first fraction by the reciprocal of the second fraction. So, (-21/4) * (4/11) = -21/11. This quotient can be written in mixed number form as -1 10/11, which is the simplified answer.
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Jessica is measuring two line segments. The first line segment is 30 cm long. The second line segment is 500 mm long. How long are the two line segments together? (answer in cm)
Answers
convert mm to cm
1mm = 0.1 cm
500 * 0.1 = 50cm
50 +30 = 80cm total length
use the multiplication table. describe a pattern you see, 5, 10, 15
Answers
Final answer:
The sequence 5, 10, 15 represents multiples of 5, where each number is 5 units apart from the last.
This pattern can also be observed in a multiplication table in the row or column of the number 5.
Explanation:
The question asks us to describe a pattern in the sequence 5, 10, 15.
This sequence represents the multiples of 5. A clear pattern that can be observed is that each number increases by 5 to get to the next multiple.
For instance, starting with 5, adding 5 gives us 10, and adding another 5 to 10 gives us 15.
This pattern continues indefinitely with the series 20, 25, 30, and so on.
All real numbers at least 3 units from -2
Answers
The first set is (-infinity, -5]. All numbers in this set are 3 or more units from -2.
The second set is [1, infinity). Same reasoning.
Drawing a diagram might help you understand this problem better.
A bird leaves its nest and travels 12 miles per hour downwind for x hours. On the return trip, the bird travels 2 miles per hour slower and has 3 miles left after x hours. What is the distance of the entire trip? How long does the entire trip take?
Answers
On the way there, 1.5x12 = 18
On the way back, 1.5x10 = 15
12x = 10x + 3
Subtract 10x from both sides
2x = 3
Divide by two on each side
x = 3/2 or 1 1/2 hours
Distance of the trip:
12 * 2 * 3/2 = 36 miles
How long does the trip take:
3/2 + 3/2 + 3/10 = 3 3/10 hours
3 hours
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Find the solution set of 3x +2y = 12 if each variable represents a positive integer.
Answers
(3/2)x-6=y
All real numbers
2×3 = 6
6+6 = 12
X = 2
Y = 3
At a school, 126 students play at least one sport. This is 40% of the students at the school. How many students are at the school?
Answers
---- x ------
126 x
At one university, the students are given z-scores at the end of the each semester, rather than the traditional gpas. the mean and standard deviation of all students' cumulative gpas, on which the z-scores are based, are 2.7 and 0.5, respectively
Answers
The students with z-scores below -1.6 would be put on probation, and the corresponding probationary GPA is 1.9.
Given data:
To translate z-scores to corresponding GPAs, you can use the formula:
GPA = (z * standard deviation) + mean
Given:
Mean (μ) = 2.7
Standard Deviation (σ) = 0.5
Let's calculate the corresponding GPAs for the given z-scores:
For z = 2.0:
GPA = (2.0 * 0.5) + 2.7
= 1.0 + 2.7
= 3.7
For z = -1.0:
GPA = (-1.0 * 0.5) + 2.7
= -0.5 + 2.7
= 2.2
For z = 0.5:
GPA = (0.5 * 0.5) + 2.7
= 0.25 + 2.7
= 2.95
For z = -2.5:
GPA = (-2.5 * 0.5) + 2.7
= -1.25 + 2.7
= 1.45
Now, to determine the corresponding probationary GPA for z = -1.6:
GPA = (-1.6 * 0.5) + 2.7
= -0.8 + 2.7
= 1.9
Hence, students with z-scores below -1.6 would be put on probation, and the corresponding probationary GPA is approximately 1.9.
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The complete question is attached below:
At one university, the students are given z-scores at the end of each semester rather than the traditional GPAs. The mean and standard deviation of all students’ cumulative GPAs, on which the z-scores are based, are 2.7 and .5, respectively.
- translate each of the following z-scores to corresponding GPA: z=2.0, z=-1.0, z=.5, z =-2.5.
- Students with z-scores below -1.6 are put on probation. What is the corresponding probationary GPA?
Emily bought a video game console and some games for $350. The video game console cost $200. Each game cost $25. How many games did Emily purchase?
Answers
25x6=150
so the answer is she bought 6 games
If bethany earned $51,740 last year, how much did she earn per week?
Answers
Charlie's father is 41 years old. His age is two years more than three times Charlie's age. What is Charlie's age?
Answers
39 divided by 3 is 13
Charlie is 13 years old
Final answer:
By setting up a linear equation, it is determined that Charlie is 13 years old based on the given information that his father is two years more than three times Charlie's age and is 41 years old.
Explanation:
The problem presented is a classic example of a linear equation in the subject of mathematics. We are given that Charlie's father is 41 years old, and his age is two years more than three times Charlie's age.
To determine Charlie's age, we can set up the equation as follows: Let x represent Charlie's age. The father's age is then described by the expression 3x + 2.
Since we know the father is 41 years old, we have:
3x + 2 = 41
Subtract 2 from both sides of the equation to isolate the terms with x:
3x = 39
Now, divide both sides by 3 to solve for x:
x = 39 / 3
x = 13
Therefore, Charlie is 13 years old.
The width of a rectangle is equal to m cm, but its length is five times greater than the width. Find the area of the rectangle.
Answers
length= 5m
Area= l×w
Area= 5m×m
Area=5m^2
(^=exponent)
The area will be 5m^2
suppose someone tells you that she has a triangle with sides having lengths 2.6,8.1 and 8.6. Is this a right triangle? why or why not? Is there an angle in the triangle larger than 90 degree?
Answers
How do we determine which length is the hypotenuse, though? Knowledge that the hypotenuse is always the longest length of a right triangle helps here, as we can clearly observe that 8.6 is the longest we've been given for this problem. The order we pick the legs in doesn't matter, since addition is commutative, and we'll get the same result regardless of the order we're adding a and b.
So, substituting our values in, we have:
(2.6)² + (8.1)² = (8.6)²
Performing the necessary calculations, we have:
6.76 + 65.61 = 73.96
72.37 ≠ 73.96
Failing this, we know that our triangle cannot be right, but we do know that 72.37 < 73.96, which tells us something about what kind of triangle it is. Imagine taking a regular right triangle and stretching its hypotenuse, keeping the legs a and b the same length. This has the fact of increasing the angle between a and b. Since the angle was already 90°, and it's only increased since then, we know that the triangle has to be obtuse, which is to say: yes, there's an angle in it larger than 90°.
Determine the unit rate. Use mental math when you can. 6 golf balls for $15. 2 dozen tennis balls for $36. 4lb meat for $18. 24 tickets for $480.
Answers
To determine the unit rate for each item, divide the total cost by the number of units. This gives us $2.50 per golf ball, $1.50 per tennis ball, $4.50 per pound of meat, and $20 per ticket.
Explanation:The question involves determining the unit rate of different items. A unit rate is the cost per one unit of an item. To calculate each unit rate, we divide the total cost by the number of units.
For 6 golf balls for $15, the unit rate is $15 ÷ 6 = $2.50 per golf ball.For 2 dozen (24) tennis balls for $36, the unit rate is $36 ÷ 24 = $1.50 per tennis ball.For 4lb of meat for $18, the unit rate is $18 ÷ 4 = $4.50 per pound of meat.For 24 tickets for $480, the unit rate is $480 ÷ 24 = $20 per ticket.These calculations can often be made using mental math, especially when dealing with simple numbers or common multiples.
9x-5y=-32 in slope intercept form
Answers
The slope intercept form of a linear equation has the following form where the equation is solved for y in terms of x:
y = a + bxb is the slopea is a constant term. It is the y intercept, the place where the line crosses the y axis.
Example 1
y = -13 + 7x
This equation is in slope intercept form. The y intercept is (0,-13) and the slope is 7.
Example 2
4x + 3y = 12
Rewrite this equation in slope intercept form.
3y = 12 - 4xThe equation is now in slope intercept form. The y intercept is (0,4) and the slope is
-4/3.
Example 3
5x - 3y - 15 = 0
Rewrite this equation in slope intercept form.
3y = -15 + 5xThe equation is now in slope intercept form. The y intercept is (0,-5) and the slope is
5/3.
Example 4
The equation is now in slope intercept form. The y intercept is (0,-7.5) and the slope is
1.5.
Find the dimensions of the rectangle with area 120 square inches and smallest possible perimeter
Answers
P=2(A/W) + 2W. This is to be minimized.
dP/dW = 2[-A/(W^2)) + 2W. But A = 120 sq in:
dP/dW = 2[-120/(W^2)) + 2W set this equal to 0 and solve for W.
Once you have W, find L: L=120/W
Let 2[-120/(W^2)) + W] = 0. Then [-120/(W^2)) + W] = 0
Multiplying all terms by W^2 gives us -120 + W^3 = 0.
w^3 = 120 cubic inches. Find the cube root to find W.
W = cube root of 120 = 4.93 inches. L = 120/W, or L = 120/4.93 inches
Summary: W = 4.93 inches and L = 24.33 inches (answer)
There are 5 slots, each containing the letters w, r, l, d or o. one letter is picked at random from each slot. what are the odds that the letters stored in these slots read the word world?
Answers
In the second slot calculate the chance of getting a o: 1/4 (notice how it's 4 not 5 because you already have one letter in the first slot so you have 4 left to choose from.)
In third slot, chance of getting a r: 1/3
In fourth slot, chance of getting a l: 1/2
In the fifth slot, if you got all the first four letters right, than you would be left with one letter, so your chances are 1/1 (100%) for the fifth slot
To calculate probability multiply all the fractions we got above: 1/5 x 1/4 x 1/3 x 1/2 x 1/1
We will then get: 1/(5x4x3x2x1) = 1/120
1/120 is the probability of the 5 slots showing the word "world"
The probability of the 5 letter slots randomly making the word 'world' is calculated by finding the product of the probability of choosing each letter correctly, which for this problem, is (1/3125).
Explanation:To calculate the probability of picking the letters 'w', 'o', 'r', 'l', 'd' in that order, we understand that we are dealing with a probability problem regarding independent events. This scenario means that the outcome of each selection does not affect the others.
Here, each slot contains 5 distinct letters. The probability of picking a specific letter correctly is 1/5 (1 way to pick a correct letter divided by 5 total letters). So, the probability of picking each letter correctly and in the order of 'world' is the product of the probabilities of choosing each letter correctly i.e P(choosing all five correct letters) = P(choosing 1st correctly) X P(choosing 2nd correctly) X P(choosing 3rd correctly) X P(choosing 4th correctly) X P(choosing 5th correctly) = (1/5) X (1/5) X (1/5) X (1/5) X (1/5) = (1/3125).
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Show that for the same shear angle, there are two rake angles that give the same cutting ratio.