Colton sold a total of 28 t-shirts and sweatshirts as part of a fundraiser for his football team. If t-shirts cost $12 each and sweatshirts cost $20 each and he raised a total of $424, how many †-shirts did he sell?
i need points
Step-by-step explanation:
mapped a quadrilateral on a coordinate plane. If she plots one segment from (–3, –3) to (3, 9) and another segment from (–5, 12) to (1, 0), are the segments parallel? Justify your reasoning.
The line segments joining the given points are not parallel.
How to find the slope of a line?In order to find the slope of a line, calculate the angle it makes with x axis as a reference. Then its slope can be determined by taking tan ratio of that angle.
Given that,
The first segment is joined from (3, -3) to (3, 9).
And, the second segment is joined from (-5, 12) to (1, 0).
In order for the segments to be parallel, their slope must be equal.
The slopes of both the segments can be found as,
First segment,
Slope = (3 - 3)/(-3 - 9)
= 0/-12
= 0
Second segment,
Slope = (-5 - 1)/(12 - 0)
= -6/12
= -1/2
Since slopes of the segments are not equal, they are not parallel.
Hence, the given line segments are not parallel.
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the angle θ is 7.2 degrees, and the circle arc s is 800 km. knowing that there are 360 degrees in a full circle what is the circumference of the surface of the earth? round to the closest 10,000 km. please explain how you came about your final solution.
The earth is 40000 kilometers around. There is no need to round off because the circumference already contains significant figures.
How do I calculate a circle's circumference?
A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14).
Given: theta angle (central) = 7.2°; arc length S = 800 km
This indicates that an 800 km long arc is extending a circle with a 7.2° center angle ( earth in this case).
By definition, "An arc's length is a portion of a circle's diameter."
Therefore, we must first establish what percentage of the circle the specified arc length represents.
360° is a complete circle.
Thus, the fraction equals 7.2°/360°, or 1/50.
As a result, the stated arc length (800km) with a 7.2° central angle is 1/50th of the entire circle.
Thus, the whole circumference is 800 x 50, or 40000 km.
Alternately, you can calculate circumference using the formula below:
360° center angle x arc length as the circumference (theta)
Values substituted: circumference 800 = 360° 7.2°
circumference = 360°, 800°, and 7.2°, or 40000 kilometers
Therefore, the earth is 40000 kilometers around. There is no need to round off because the circumference already contains significant figures.
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Which correctly shows how to use the gcf and the distributive property to find an expression equivalent to ?.
The correct option B. 9(5 + 8) ; is the equivalent expression to 45 + 72 using the GCF and the distributive property.
Explain the distributive property?The distributive property states that multiplying the sum of 2 or more operand by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.A mathematical statement made up of variables, constants, and mathematical operators is called an expression.
The formula is 45 + 72.
45 and 72 divided by one is three and nine.
The GCF is nine.
The largest number that evenly divides two or even more given numbers is known as the greatest common factor.
You can write the phrase as,
9 ( 5 + 8)
45 +72 = 9 ( 5 + 8)
Thus, the Distributive property was used to factor this.
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The correct question is-
Which correctly shows how to use the GCF and the distributive property to find an expression equivalent to 45 + 72?
A. 3(15 + 24)
B. 9(5 + 8)
C. (5)(9) + (2)(36)
D. (3)(15) + (8)(9)
maya drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took hours. when maya drove home, there was no traffic and the trip only took hours. if her average rate was miles per hour faster on the trip home, how far away does maya live from the mountains? do not do any rounding.
Maya drove on the mountains for her trip. Due to traffic, her average rate of miles per hour was faster at the time of coming back to her home than going on her trip. Thus, The distance between where she lives and the mountains is
288 miles .
Let's consider that Maya live x miles from the mountains.
Let her rate to mountains be y miles/h.
we have given that
Driveing time taken by Maya going from home to trip location= 9 hours due to traffic
total return time taken by her = 4 hours
average rate = 40 miles/hour
Using rate formula,
Rate = distance/time
=> distance (d) = rate (r) × time (t)
so, x/y = 9
=> x=9y --(1)
Return trip 4 hours then rate = y+40
=> x/(y+40) =4 --(2)
using Substitution method, x= 3 substitute in (2)
=> 9y/(y+40)=4
=> 9y=4y+160
=> 9y-4y=160
=> 5y=160
=> y= 160/5
=> y=32
Now, x=9y
x=9×32= 288 miles
Hence, distance to the mountain is 288 miles.
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Complete question:
Maria drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 9 hours. When Maria drove home, there was no traffic and the trip only took 4 hours. If her average rate was 40 miles per hour faster on the trip home, how far away does Maria live from the mountains?
Do not do any rounding.
what is the answer to -2a+5a=-3a
Answer: a=0
Step-by-step explanation:
-2a + 5a = -3a
3a = -3a
a= 0
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One week, magan earned $162. 00 at his job when he worked for 9 hours. If he is paid the same hourly wage, how much would he make the next week if he worked 19 hours?.
Answer: $342
Step-by-step explanation:
We take 162.00 divided by 9 = $18 / h
To find the salary of 19 hours we just need to take 18 times 19 = $342
UGGGHHHH! THIS IS FIND SLOPE INTERCEPT AND I CAN’T FIGURE IT OUT!
The linear equation written in the slope-intercept form is:
y = -x - 5
How to find the slope?A linear equation can be written in the slope-intercept form as:
y = m*x + b
Where m is the slope and b is the y-intercept.
Particularly, if the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope of the line is written as:
m = (y₂ - y₁)/(x₂ - x₁)
Here we can use the first two points on the table (or any you want) to find the slope:
(-1, -4) and (3, -8)
m = (-8 + 4)/(3 + 1) = -1
The slope is -1, so the line is something like:
y = -x + b
To find the value of b we can use another of the points on the table, if we use (7, -12) then we must have:
-12 = -7 + b
-12 + 7 = b
-5 = b
The linear equation is:
y = -x - 5
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(A) Prove that the opposite sides of the rectangle are congruent.
Use Distance Formula: v(x2 - x1)^2 + (y2 - y1)^2
(B) Prove the diagonals of your rectangle are congruent.
(C) Using the slopes for each side, prove there are 4 right angles on the rectangle.
**Please Show All Work**
A. Using the distance formula, we can state that the opposite sides are congruent because AD = BC = √10 units and AB = CD = √40 units.
B. The diagonals are equal, AC = BD = √50 units.
C. Based on the slopes of each side, there are 4 right angles on the rectangle.
What is the Distance Formula?The distance formula is used to find the distance that exist between tow points that are on a coordinate plane. The formula is: d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
What is the Slope of a Line?
Slope = change in y / change in x.
A. The coordinates of each of the vertices of the rectangle are:
A(1, 2)
B(7, 4)
C(8, 1)
D(2, -1)
Use the distance formula to find AB, CD, BC, and AD.
AB = √[(7−1)² + (4−2)²]
AB = √40
CD = √[(2−8)² + (−1−1)²]
CD = √40
BC = √[(8−7)² + (1−4)²]
BC = √10
AD = √[(2−1)² + (−1−2)²]
AD = √10
Therefore, the opposite sides are congruent because AD = BC = √10 units and AB = CD = √40 units.
B. The diagonals are AC and BD. Find their lengths using the distance formula:
AC = √(8−1)² + (1−2)²]
AC = √50 units
BD = √[(2−7)² + (−1−4)²]
BD = √50 units
Therefore, the diagonals are equal, AC = BD = √50 units.
C. Find the slope of AB, CD, BC, and AD:
Slope of AB = change in y / change in x = rise/run = 2/6 = 1/3
Slope of CD = 2/6 = 1/3
Slope of BC = -3/1 = -3
Slope of AD = -3/1 = -3
-3 is the negative reciprocal to 1/3, this means that, if the two lines that meet at a corner have these two slope, then they will form a right angle because they are perpendicular to each other.
Therefore, there are 4 right angles on the rectangle.
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Tim has 1 1/4 kilograms of raisins. He uses 1/6 of the raisins in his trail mix. How many kilograms of raisins did Tim use?
Tim will use 5/24 kilograms of raisins in his trail mix.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Tim has 1(¹/₄) kilogram of raisins. He uses 1/6 of the raisins in his trail mix.
The weight of the raisins will be calculated as,
Weight = 1(¹/₄) x 1 / 6
Weight = ( 5 / 4 ) x ( 1 / 6 )
Weight = 5 / 24 kg
Therefore, Tim will use 5/24 kilograms of raisins in his trail mix.
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if you wish to test whether these data are sufficient to indicate that the mean for population 2 is larger than that for population 1, what are the appropriate null and alternative hypotheses? define any symbolys you see
at 0.1 level of significance, we can conclude that these data are sufficient to indicate that the mean for population 2 is larger than that for population 1.
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 10 - 1 = 9
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (- 3.7 - 0)/(2.71/√10)
t = - 4.32
We would determine the probability value by using the t test calculator.
p = 0.00097
Since alpha, 0.1 > than the p value, 0.00097, then we would reject the null hypothesis. Therefore, at 0.1 level of significance, we can conclude that these data are sufficient to indicate that the mean for population 2 is larger than that for population 1.
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HELP ASAP PLEASE WITH EXPLINATION!!
Chris earns $7.00 per hour working on the weekends he needs at least $210.00 for a new cell phone. How many hours, h, doe Chris need to work on the weekends to buy a new phone
Answer:
So...
Step-by-step explanation:
He earns $7.00 per hour, and he needs $210.00. H represents hours.
7.00 every hour
So 7.00 x 2 is 14
7.00 x 10.00 is 70
7.00 x 30 is 210. So after 30 hours he will be able to buy his phone. He should buy his phone on black friday. But now its too late.
30 points Please get it Right lol
Graph the piecewise function.
Answer:
see attached
Step-by-step explanation:
You want a graph of the piecewise function ...
[tex]f(x)=\begin{cases}x&\text{if $x\le -1$}\\-3x+2&\text{if $-1 < x < 4$}\\4&\text{if $x\ge 4$}\end{cases}[/tex]
GraphThe graph is attached.
For x ≤ -1, the graph is a line with slope 1. If it were allowed to continue, it would pass through the origin. It terminates in a closed dot at (-1, -1)
For -1 < x < 4, the graph is a line with slope -3 through point (0, 2) on the y-axis. It has open circles at both ends, at points (-1, 5) and (4, -10).
For x ≥ 4, the line is horizontal at y=4. It has a closed dot at (4, 4).
__
Additional comment
The dot at the end of an interval is closed if the "or equal to" case is included (≤ or ≥). If it is not (< or >), then the dot is an open circle.
The slope is the ratio of "rise" to "run". It is the number of grid squares the line moves up (+) or down (-) for each grid square to the right.
140 is what percent
less than 160 ? PLSASE HELP
Answer:
The answer should be 12.5%
Please help me with the question in the picture
Answer:
7.5
Step-by-step explanation:
W -- X -- Y ----- Z
We are given that :
Y is the midpoint of WZ meaning that WY = YZX is the midpoint of WY meaning that WX = XY WY = 5Given this we want to find XZ
XZ consists of XY and YZ so we must find the length of the individual segments.
Finding YZ
Here, we know that YZ = WY as y is the midpoint of WZ. If WY = 5 then YZ also = 5
Finding XY
Given that WY = 5 and that X is a midpoint of WY we know that the segments WX and XY = WY and are congruent.
In other words we can say that 2XY = WY
==> WY = 5
2XY = 5
==> divide both sides by 2
XY = 2.5
Finding XZ
Again, XY + YZ = XZ
We have XY = 2.5 and YZ = 5
Hence, 2.5 + 5 = XZ
XZ = 7.5
Answer:
XZ = 7.5
Step-by-step explanation:
A drawing is sometimes very helpful.
Start by drawing a segment with endpoints W and Z.
+--------------------------------------------+
W Z
Y is the midpoint of WZ. Draw point Y in between W and Z and the same distance from both W and Z.
+---------------------+--------------------+
W Y Z
X is the midpoint of WY. Draw X between W and Y, and the same distance to W and Y.
+----------+----------+--------------------+
W X Y Z
Because of the midpoints, we know that:
WX = XY
WY = YZ
WY = 5
WX and XY are each half of WY, so WX = XY = 5/2 = 2.5
WY = YZ = 5
XZ = XY + YZ
XZ = 2.5 + 5
XZ = 7.5
For the function ƒ(x) = 5 (x³ – 6), find ƒ−¹(x).
○ ƒ˜¹(x) = (²16) ³
○ f−¹(x) = 2³+6
○ ƒ˜¹(x) = ( ² + 6) ³
○ ƒ−¹(x) = (x+6)³
5
Submit Answer
find the perimeter of the window to the nearest hundredth
The perimeter of the window to the nearest hundredth will be;
⇒ 102.8 cm
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The shape of window is semicircle.
And, The radius of window (r) = 20 cm
Now,
We know that;
The perimeter of semicircle = πr + 2r
Here, The radius of window (r) = 20 cm
So, We get;
The perimeter of the window = πr + 2r
= 3.14 x 20 + 2 x 20
= 62.8 + 40
= 102.8 cm
Thus, The perimeter of the window to the nearest hundredth will be;
⇒ 102.8 cm
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The sampling distribution for a goodness of fit test is the a. Poisson distribution b. t distribution c. normal distribution d. chi-square distribution
The sampling distribution for a goodness of fit test is the
d. chi-square distributionWhat is chi-square distribution?A continuous distribution with degrees of freedom is a chi-square distribution. It is used to describe how a sum of squared random variables is distributed.
When comparing categorical variables from a random sample, the statistical test known as chi-square is used to assess the degree of fit between the predicted and actual results.
We can therefore conclude that chi-square distribution is the sampling distribution for a goodness of fit test
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Multiply (4m - 9)(3m - 11) using tabular/grid method or foil method or distributive property
Answer:
[tex]12m^2-71m+99[/tex]
Step-by-step explanation:
I will use distributive property
(4m-9)(3m-11)
4m(3m)+4m(-11)-9(3m)-9(-11)
12m^2-44m-27m+99
Combine like terms
12m^2-71m+99
Hopes this helps please mark brainliest
a business major needs 3 humanities courses to graduate. they can be selected from 29 courses offered. how many ways can the 3 courses be selected?
The number of ways 3 courses can be selected is 3654.
What are the Permutation and Combination?
Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement. When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.
Total no. of courses available = 29
Courses needed to graduate = 3
No of ways these courses can be selected:
= ²⁹C₃
= 29!/ [(29-3)! - 3!]
= 29! / 26! 3!
= 29 * 28 * 27 * 26!/ 26! 3*2
= 29* 14* 9
= 3654
So, the number of ways 3 courses can be selected is 3654.
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two times a number is divided by 3 more than the number. if the result is 7, then what was the original number?
The original number is -21/5 or -4.2 which is divided by 3 more than the number.
What is an equation?In mathematics, an equation is a statement or formula which shows two expressions having equal value and connected by an equal sign. The two expressions consist of variables and/or numbers.
For solving the question we have to form an equation.Let the number be 'x' Two times the number = 2x3 more than the number = x + 3
According to the question,two times a number is divided by 3 more than the number is equal to 7 which means 2x / (x+3) = 7
By applying cross multiplication,2x = 7 × ( x+3)2x
= 7x + 7×32x
= 7x + 212x - 7x
= 21-5x = 21x = 21/ (-5)x
= -4.2
Hence the original number is -4.2
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Please answer this is due today
"In a fruit salad, there are 12 strawberries, 14 grapes, and 4 mangos. Find the ratio of mangos to grapes. Write the ratio using a colon in the simplest form"
Answer:
The ratio of mangos to grapes is 2:7.
Step-by-step explanation:
The original ratio of mangos to grapes would be 4:14. When it says mangos to grapes, it means mangos first, then grapes. If it said grapes to mangos, the grapes would go first. But, in this case the mangos go first. Now, we don't worry about the strawberries because it says to find the ratio of mangos to grapes, which is 4:14. Now, it says to simplify it to the simplest form. So, we can do this by dividing both numbers by the same number down as far as they can go as a whole number (a number without a decimal):
4 ÷ 2 = 2
14 ÷ 2 = 7
So, this is as far as we can go. So, our final answer is 2:7.
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Answer:
2:7
Step-by-step explanation:
4 mangos for every 14 grapes
the ratio right now is 4:14 this can be simplified by dividing by 2
4 divided by 2 = 2 ( 2 x 2 = 4 )
14 divided by 4 = 7 ( 7 x 2= 14)
Now the ratio is 2:7, or 2 mangos for every 7 grapes we know this is right because in order to use the amount the recipe calls for you need to double the answer
(adding separately is easier)
2+2 = 4
7+7 = 14
= 4:14
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
25:5
Answer:
5
Step-by-step explanation:
25/5 = 5/1 = 5
What is the solution of the system of equations? Explain.
y = x +4
2
2y + 4 = x
The solution of the system of equations:
y = x + 422
y + 4 =x
is the point (-88, -46)
How to solve the system of equations?Here we have the system of equations:
y = x + 42
2y + 4 =x
To solve the system, we can replace the first equation into the second one:
2*(x + 42) + 4 = x
2x + 84 + 4 = x
2x + 88 = x
2x - x = -88
x = -88
And the value of y is:
y = x + 42
y = -88 + 42 = -46
The solution is the point (-88, -46).
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what is the value of x in this triangle? enter your answer in the box. x
By using trigonometry, it can be calculated that
Value of x is 23.775
What is trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions. They are
[tex]sin \theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]
[tex]sin\theta = \frac{perpendicular}{hypotenuse}[/tex]
[tex]cos\theta = \frac{base}{hypotenuse}[/tex]
[tex]tan\theta = \frac{perpendicular}{base}[/tex]
[tex]cot\theta = \frac{base}{perpendicular}[/tex]
[tex]sec\theta = \frac{hypotenuse}{base}[/tex]
[tex]cosec\theta = \frac{hypotenuse}{perpendicular}[/tex]
Trigonometry is a very important tool in mathematics.
Here, trigonometry is used
From the figure,
cos 18 = [tex]\frac{x}{25}[/tex]
0.951 = [tex]\frac{x}{25}[/tex]
x = 0.951 [tex]\times[/tex]25
x = 23.775 cm
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Complete Question
what is the value of x in this triangle? enter your answer in the box. x
x = cm
A right triangle. The hypotenuse is labeled as 25 centimeters. The base is labeled as x. The alternate base angles are labeled as right angle and 18 degrees, respectively.
In tryouts for the olympics, a speed skater had times of 44. 64, 43. 45, 42. 79, and 42. 28 seconds. Find the average time. (hint: add the numbers and divide by 4. ).
The average time of the Olympic speedskated is 43.29 units.
What do we mean by average?An average, which is frequently the sum of the numbers divided by the total number of the numbers in the group, is a single number that is selected to describe a group of numbers in simple English.
For example, the average of the numbers 2, 3, 4, 7, and 9 is 5.
The four sorts of averages that we recognize are mean, mode, median, and range.
Although the others are our most popular "measures of central tendency," range is actually a measure of spread or distribution.
So, the average time is calculated as follows:
We have: Time: 44.64,43.45,42.79 and 42.28
The formula for average mean: ∑ₓ/n
Where ∑ₓ is the sum of observations and n is the number of observations.
Now, calculate the average time:
Average = 44.64+43.45+42.79+42.28/4
Average = 173.16/4
Average = 43.29
Therefore, the average time of the Olympic speedskated is 43.29 units.
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Trapezoid WXYZ is isosceles. Angle WZY measures (8x – 3) and angle XYZ measures (7x + 2). Find the measure of angle WZY.
The measure of angle WZY of the Trapezoid WXYZ is; 37
How to find the angle of the trapezoid?
We are told that the Trapezoid WXYZ is isosceles. This means that there would be two angles that are equal.
Thus, we can see that Side WZ and XY are equal and as such, it means that Angle WZY is congruent to angle XYZ.
We are told Angle WZY measures (8x – 3) and angle XYZ measures (7x + 2). Thus;
(8x – 3) = (7x + 2)
8x - 7x = 2 + 3
x = 5
Thus;
Angle WZY = (8(5) – 3)
Angle WZY = 37°
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simplify (−4r5)(2r8)
Answer: -8r^13
Step-by-step explanation: We just need to take those numbers multiplied by each other. -4 timed 2 = -8. r^5 timed r^8 = r^13, we just add both because they have the same base and multiple a square is the same as adding them together.
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Use the fact that the trigonometric functions are periodic to find the exact value of the given expression. Do not use a calculator.
sec.(25π/4)
Subtract full rotations of 2π until the angle is greater than or equal to 0 and less than 2π
sec(π4) – trigonometry value
The exact value of trigonometry - sec(π4) is 2√2.
Multiply 2√2 by √2.
2⋅√2⋅2
Combine and simplify the denominator.
2√2
Cancel the common factor of 2.
√2
There are various ways to display the outcome.
Exact Form:
√2
Decimal Form:
1.41421356…
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2. consider the trapezoid in the previous problem. locate the center of mass of the trapezoid. remember to again break the trapezoid into horizontal or vertical strips.
Calculations in mechanics involving masses dispersed in space, such as the linear and angular momentum, benefit from using the centre of mass as a reference point.
The centre of mass of the trapezoid can be found by breaking it into two trapezoids and finding the centre of mass of each. The centre of mass of the first trapezoid is located at (3, 5). The centre of mass of the second trapezoid is located at (9, 5). Therefore, the centre of mass of the trapezoid is located at (6, 5).
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