Answer:
Step-by-step explanation:
First, we will find the midpoint for the x - coordinate first.
Midpoint (x) = [tex]\frac{-1+(-6)}{2} \\=\frac{-1-6}{2} \\=\frac{-7}{2} \\=-3.5[/tex]
Now we will find the midpoint for the y - coordinate.
Midpoint (y) = [tex]\frac{-6+5}{2} \\=\frac{-1}{2} \\=-0.5[/tex]
Therefore from these 2 values we know that the midpoint of this 2 points is (-3.5,-0.5)
Two student clubs were selling t-shirts and school notebooks to raise money for an upcoming school event. In the first few minutes, club A sold 3 t-shirts and 2 notebooks, and made $19. Club B sold 1 t-shirt and 1 notebook, for a total of $8. Use the given matrix equation to solve for the cost of t-shirts and notebooks that were sold. Explain the steps that you took to solve this problem.
A matrix with 2 rows and 2 columns, where row 1 is 3 and 2 and row 2 is 1 and 1, is multiplied by matrix with 2 rows and 1 column, where row 1 is x and row 2 is y, equals a matrix with 2 rows and 1 column, where row 1 is 19 and row 2 is 8.
Using a system of equations, it is found that the cost of a t-shirt is of $3 and the cost of a notebook is of $5.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The variables are given as follows:
Variable x: Cost of a t-shirt.Variable y: Cost of a notebook.Considering the costs of the purchases of Clubs A and B, the matrices give the equations as follows:
3x + 2y = 19.x + y = 8 -> y = (8 - x).Hence, replacing the second equation into the first:
3x + 2(8 - x) = 19
x = 3.
y = 8 - x = 8 - 3 = 5.
The cost of a t-shirt is of $3 and the cost of a notebook is of $5.
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What is the domain indicated on the graph for each
portion of the piecewise function?
-2,
2x + 1,
--—-x,
f(x)=
Domain 1st piece
Domain 2nd piece
Domain 3rd piece
Step-by-step explanation:
try this option, all the details are in the attachment.
The square shown has a perimeter of 32 units. The square is rotated about line k. what is the circumfrence of the base
The circumference equal to 25 units
What is perimeter of square?The perimeter of square is 4 times the side.
P= 4* side
The perimeter of the square,
4x = P
Now P is = 32 units then,
32 units = 4(x)
x = 8 inches
So, the diameter of the cylinder formed by the rotation of 8 inches
Now, the circumference of the base is
C = 2πr = πD
If r =8 inches
C = π(8 units) = 8π units
C = 8(3.14) = 25.12 units
Hence, the circumference equal to 25 units
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Solve x 6x+2=2x-1 give your answer as a fraction in its simplest form
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{6x + 2 = 2x - 1}[/tex]
[tex]\huge\textbf{SUBTRACT 2x to BOTH SIDES:}[/tex]
[tex]\mathbf{6x + 2 - 2x = 2x - 1 - 2x}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{4x + 2 = -1}[/tex]
[tex]\huge\textbf{SUBTRACT 2 to BOTH SIDES:}[/tex]
[tex]\mathbf{4x + 2 - 2 = -1 - 2}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{4x = -3}[/tex]
[tex]\huge\textbf{DIVIDE 4 to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{4x}{4} = \dfrac{-3}{4}}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{x = \dfrac{-3}{4}}[/tex]
[tex]\mathbf{x = -\dfrac{3}{4}}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = -\dfrac{3}{4}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assigiment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]A freight train was supposed to travel 1300 miles in 50 hours. When the train had traveled 0.4 of this distance, it was delayed by 4 hours. What should the new speed of the train be to arrive on time?HELLPASAP
Answer:
The answer is 30 miles per hour
Step-by-step explanation:
1) From the question we can calculate the initial speed of the train
Initial speed = 1300 miles / 50 hours
= 26 miles / hour
2) Next, we can calculate the amount of distance already traveled:
Distance traveled = 1300 * 0.4
= 520 miles
3) Now let's calculate the amount of time it took to travel the 520 miles:
From point no. 1 we saw that it was traveling at the speed of 26 miles/ hour, so let's calculate the time elapsed.
Time elapsed = 520 miles / 26 hours
= 20 hours
But then again the text states the train was delayed by 4 hours, therefore the total time elapsed was 24 hours
4) Now to find the new speed required to arrive on time, we need to calculate how many hours and distance are left:
From point no. 2 we calculate the distance left
Distance left = 1300 - 520
= 780 miles
From point no. 3 we can calculate the amount of time left:
Time left = 50 - 24
= 26 hours
Finally, we can find the new speed required to arrive on time:
New speed = 780 miles / 26 hours
= 30 miles / hour
How many different strings can be made by shuffling the letters in DISCRETEMATHS?
Answer:
I found 14 but their might be more!
hope that helps! :)
Step-by-step explanation:
What are the medians for the height and weight distribution, respectively?
The median for height is: 167
The median for Weight is: 183
What is the Median of a Data Set?The middle value or the average of the two middle value of an ordered data set is the median of the data.
Given the following data:
Height: 178, 163, 174, 186, 154, 167, 167, 181, 159, 165, 177, 191, 158
Arranged in an ordered form, we would have:
54, 158, 159, 163, 165, 167, [167,] 174, 177, 178, 181, 186, 191
The middle value is 167. The median for height is: 167.
Weight: 157, 163, 190, 187, 183, 173, 184, 189, 193, 192, 177, 173, 168
Arranged in an ordered form, we would have:
157, 163, 168, 173, 173, 177, [183,] 184, 187, 189, 190, 192, 193
The middle value is 183. The median for weight is: 183.
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The difference......
Answer:
[tex] log_{7}(3) [/tex]
Step-by-step explanation:
According to the
Law of logarithms,[tex] log_{7}(18) \: - log_{7}(6) \\ \\ = \frac{ log_{7}(18) }{ log_{7}(6) } = log_{7}(3) [/tex]
About 145 out of 500 students prefer walking instead of
riding the bus to school. About what percent of the
students prefer walking?
30%
50%
70%
145%
Answer:
30%
Step-by-step explanation:
[tex]\frac{145}{500} = 0.29[/tex] ≅ 0.30 or 30%
A
<
Lennox had been scheduling employees based on the assumption that the
following distribution represented when people made purchases in his store.
Time slot
Predicted
percentage
8 a.m.-12 p.m.
25%
12-4 p.m.
40%
4-8 p.m. 8-12 a.m.
25%
10%
He took a random sample of 300 purchases and recorded their time slot so he
could test whether this was an accurate distribution. Here are his results:
Time slot 8 a.m.-12 p.m. 12-4 p.m. 4-8 p.m.
Purchases
75
120
90
Choose 1 answer:
8-12 a.m.
15
He wants to use these results to carry out a x² goodness-of-fit test to determine
if the distribution of time slots of the purchases disagrees with his assumed
distribution.
What are the values of the test statistic and P-value for Lennox's test?
The test value and the p value for the probability are 10.5 and 0.0148.
How to illustrate the probability?Based on the information, the observed and expected values will be:
Observed. Expected
75. 75
100. 120
90. 75
15. 30
The p value based on the test statistic from the distribution table will be 0.0148.
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DUE IN 3MINUTes
There is a strong positive linear correlation between rainfall and the number
of peaches a tree produces. Does this mean that more rainfall causes peach
trees to produce more fruit?
A. No. Any number of factors could also be affecting the number of
peaches produced.
B. No. Since rainfall and number of peaches are linearly correlated,
this means that more rainfall causes peach trees to produce less
fruit.
C. Yes. Since rainfall and number of peaches are positively
correlated, this means that more rainfall causes peach trees to
produce more fruit.
D. Yes. Since rainfall and number of peaches are linearly correlated,
this means that more rainfall causes peach trees to produce more
fruit.
Answer:
A. No.
Step-by-step explanation:
The job of science is to explain relationships in the real world. Scientists do this by making observations, forming theories regarding relationships, and conducting experiments to test those theories.
An observation of correlation may result in a theory that one of the correlated phenomena causes another. The correlation, by itself, does not demonstrate causation. Any number of other factors could be involved.
What is the ratio of 12 blue marbles and 20 red marbles
Answer:
12:20
Step-by-step explanation:
i hope the answer will help you
Helppppppp pleaseeeee
Answer:
is it asking how many times u would get then number 5 when u roll or asking how you would expect for the first 5 rolls?
Use
f(x) = 2x − 3
and
g(x) = 4 − x2
to evaluate the expression.
The equation based on the information given will be x⁴ + 8x² - 12.
How to compute the value?It should be noted that from the information given, the expression to compute will be:
= g - g(x)²
This will be:
= 4 - (4 - x²)²
= 4 - (4 - x)(4 - x)
= 4 - (15 - 8x² + x⁴)
= x⁴ + 8x² - 12
The complete question is:
Use f(x) = 2x − 3 and g(x) = 4 − x² to evaluate the expression g - g(x)².
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The table below shows the number of correct answers that students gave on a recent 5-question quiz. Which of the following statements is true? Number Correct 1 2 3 4 5 3 46 9 8 Frequency
The true statement about the number of correct answers is that the: A. median = mode.
How to calculate the mean?Mathematically, the mean for the number of correct answers can be calculated by using the following formula:
Mean = [F(x)]/n
Total frequency, n = 3 + 4 + 6 + 9 + 8 = 30.
F(x) = [(1 × 3) + (2 × 4) + (3 × 6) + (4 × 9) + (5 × 8)] = 105.
Mean = 105/30
Mean = 3.5.
For the median, we have:
The median for the number of correct answers is the average of the 15th and 16th number:
Median = (4 + 4)/2
Median = 8/2
Median = 4.
For the mode, we have:
The mode for the number of correct answers is the answer with the highest frequency, which is 4 with a frequency of 9.
Therefore, the true statement about the number of correct answers is that the median is equal to mode.
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Complete Question:
The table below shows the number of correct answers that students gave on a recent -question quiz. Which of the following statements is true?
A. median = mode
B. mode > median
C. mode < mean
D. mean > median Reset Selection
The table shows a hot air balloon's height h , in feet, during a descent at various times t , in seconds.
Part A: Use the table's first two ordered pairs to find the hot air balloon's rate of change.
Part B: Is the rate of change constant? Explain.
Part C: What was the hot air balloon's height at the time the descent began?
Part D: Write , as a linear function of
.
Using a linear function, we have that:
A. The rate of change is of -12 feet per second.
B. The rate of change is constant.
C. The initial height is of 1210 feet.
D. The linear function is: h(t) = -12t + 1210.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.From the table, when x changes by 5 seconds, the height decreases by 60 feet, hence the slope is given by:
m = -60/5 = -12 feet per second.
Hence the function is:
h(t) = -12t + b.
When t = 5, h(t) = 1150, hence we use this to find the initial height.
h(t) = -12t + b.
1150 = -12(5) + b.
b = 1210.
Hence the linear function is:
h(t) = -12t + 1210.
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A rectangular prism with a base that is
5 inches by 4 inches and a height of 15 inches.
The surface area and the volume of the rectangular prism are 310 in² and 300 in³, respectively.
How to find the volume of a right rectangular prism?Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:
V = a × b × c unit³
The surface area of the prism = 2[(5×4)+(15×4)+(15×5)]
= 310 inches²
The volume of the prism = 5 × 4 × 15
= 300 in³
Hence, the surface area and the volume of the rectangular prism are 310 in² and 300 in³, respectively.
The complete question is:
A rectangular prism with a base that is 5 inches by 4 inches and a height of 15 inches. Find the volume and the surface area of the rectangular prism?
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The following graph shows a proportional relationship.
What is the constant of proportionality between y and x in the graph?
Answer:
[tex]k=2[/tex]
Step-by-step explanation:
The constant of proportionality is given as [tex]k=\frac{y}{x}[/tex] .
Notice that when [tex]x=2[/tex] it follows that [tex]y=4[/tex].
Substitute [tex]x=2[/tex] and [tex]y=4[/tex] into the formula for the constant:
[tex]k=\frac{4}{2}=2[/tex] .
Therefore, the constant is equal to 2.
5. The function h(t) = 1 + 4t - 1.86t? models the height of a rock thrown upward on the planet Mars, where h(t) is height in meters and t is time in seconds. Use a graph to determine:
a. the maximum height the rock reaches
b. how long the rock will be above the surface
The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
From the graph of the function h(t) = 1 + 4t - 1.86t²:
The maximum height the rock reaches 3.15 feet.
Time spent on air = 2.38 - (-0) = 2.38 seconds
The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds
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Find the largest rational number r for which 5r ≤ 33.
Answer:
33/5 or 6.6
Step-by-step explanation:
Well the most 5r can be is 33, since it has the underline under it, so it's less than or equal to.
So set 5r equal to 33
5r = 33
Divide both sides by 33
r = 33/5
You can leave it in this form or convert it to a decimal which is 6.6
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
[tex]\mathsf{5r \leq 33}[/tex]
[tex]\huge\textbf{Simplifying it:}[/tex]
[tex]\mathsf{5r \leq 33}[/tex]
[tex]\huge\textbf{Divide \boxed{5} to both sides:}[/tex]
[tex]\mathsf{\dfrac{5r}{5}\leq \dfrac{33}{5}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{r \leq \dfrac{33}{5}}[/tex]
[tex]\mathsf{r \leq 6 \dfrac{3}{5}}[/tex]
[tex]\mathsf{r \leq 6.60}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{r \leq \dfrac{33}{5}}}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
[tex]\large\textsf{The graph will be labeled down below for you :)}\downarrow[/tex]
Based only on the information given in the diagram which congruence theorems or postulate could be given as reasons why LMN and OPQ
The congruence theorems or postulates could be given as reasons why LMN is congruent to OPQ are LA and AAS.
What is congruence theorems?Congruence theorems is one that explain that in a case whereby three sides of two triangles are equal to another, we can say they are congruent to each other.
From the given figure, there are two angles as well as one non-included side which is seen to be a congruent.
According to LA theorem , a triangle is congruent in a case whereby, leg as well as an acute angle of one right triangle of two right triangles are congruent to each other.
AAS theorem also explains that incase two angles and any of the side of a triangle are congruent to each other , the triangles are congruent.
Therefore, with these theorem, congruence theorems or postulates could be given as reasons why LMN is congruent to OPQ are LA and AAS.
CHECK THE FIQURE FOR THE COMNPLETE QUESTION
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1. A(–6 , 2) , B(4 ,7) are endpoints of a line segment.
(2) a) Calculate the length of AB.
(2) b) Calculate the slope of AB.
(2) c) Calculate the coordinates of the midpoint of AB.
(2) 2. Determine the radius of the circle .
State the answer as an exact number, and as a decimal rounded to 1 decimal place.
(2) 3 Write the equation of a circle with centre (0, 0) that passes through the point (5, –3)
The length of the line AB as described by points A and B in the task content is; √125.
What is the length of the line?a) The length of AB as described is;
AB = √((7-2)² + (4-(-6))²)
AB = √(25 + 100) = √125.
b) The slope of AB is;
Slope, m = (7-2)/(4-(-6)) = 5/10
Slope = 1/2.
c). The coordinates of the midpoint of AB are;
x = (4+(-6))/2 = -1
y = (7+2)/2 = 4.5
The midpoint is; (-1, 4.5).
2) The radius of the circle as described with centre (0, 0) that passes through the point (5, –3) is;
Radius = √((5-0)² + (-3-0)²)
Radius = √(25+9) = √34 = 5.8
3) Hence, the equation of a circle with centre (0, 0) that passes through the point (5, –3) is;
(x-5)² + (x-3)² = 5.8².
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In AUVW, m/U = (9x - 8)°, m/V = (2x + 2)°, and m/W = (3x + 4)º.
Find m/V.
Answer:
m∠V = 28°
Step-by-step explanation:
In ΔUVW:
m∠U = (9x - 8)°m∠V = (2x + 2)°m∠W = (3x + 4)°To find the measure of angle V, first find the value of x.
Interior angles of a triangle sum to 180°.
⇒ m∠U + m∠V + m∠W = 180°
⇒ (9x - 8) + (2x + 2) + (3x + 4) = 180
⇒ 9x + 2x + 3x - 8 + 2 + 4 = 180
⇒ 14x - 2 = 180
⇒ 14x = 182
⇒ x = 13
Substitute the found value of x into the expression for angle V:
⇒ m∠V = 2(13) + 2
⇒ m∠V = 26 + 2
⇒ m∠V = 28°
Therefore, the measure of angle V is 28°.
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calculate the value of the sample variance of 13,−2,−2,−2,13,13,−5
Answer:
13, -2
Step-by-step explanation:
Use the table to work out the values of a, b,
C, and d.
X
-3
-2
-1
0
1
2
3
y = 5x
—
a
3x² + 3
- 19
-5
3
b
C
d
During the first year of life, a whale gains about 30 tons of weight what is the average weight gain per month?
A rectangle has length of 10 mm. • and breadth 7mm calculate its perimeter YW
Answer:
34 mm
Step-by-step explanation:
P = 2 x (L + B) for a rectangle
P = 2 x (10 + 7) = 2 x 17 = 34
PLEASE ANSWER ,in terms of the trigonometric ratios for BCD,what is the lenght of BD? insert text on the triangle in geogebrea to show the lenght of BD. take a screenshot of the triangle with the text,save it,and insert the image in the space below
By applying the law of sine, the length of side BD is equal to 9.05 cm and the image of right-angled triangle BCD is shown in the image attached below.
How to calculate the length of BD?In order to determine the length of side BD, we would apply the law of sine because both side BD and side BC represent the opposite side and hypotenuse of right-angled triangle BCD respectively.
Mathematically, the law of sine is given by this mathematical expression:
sin(θ) = Opp/Hyp
Where:
Opp is the opposite side of a right-angled triangle.Hyp is the hypotenuse of a right-angled triangle.θ is the angle.Substituting the parameters into the formula, we have;
sin(θ) = BD/BC
sin(74) = BD/9.41
Cross-multiplying, we have:
BD = 9.41 × sin(74)
BD = 9.41 × 0.9613
BD = 9.05 cm.
By applying the law of sine, the length of side BD is equal to 9.05 cm and the image of right-angled triangle BCD is shown in the image attached below.
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The function f(x) is graphed. It represents a translation of the square root function g(x) = .
What equation represents the graph of f(x)?
f(x) =
f(x) =
f(x) = – 1
f(x) = + 1
The equation that represents the graph of f(x) is [tex]f(x) = \sqrt {x - 1[/tex]
How to determine the equation of f(x)?The complete question is in the attached image
The parent square root function is:
[tex]g(x) = \sqrt x[/tex]
From the graph,
g(x) is shifted one unit right to get f(x)
This is represented as:
f(x) = g(x - 1)
So, we have:
[tex]f(x) = \sqrt {x - 1[/tex]
Hence, the equation that represents the graph of f(x) is [tex]f(x) = \sqrt {x - 1[/tex]
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2. What is the radius of a circle (rounded to the nearest tenth) that has a circumference of 87 cm?
O 10.5
27.7
13.8
5.3
3.
A = pi x r^2
48 = 3.141... x r^2
÷ by value of pi
15.278... = r^2
Square root the ans, to get r
Thus, R = 3.908..... So, radius is 3.9
2.
Circumference = pi x diameter
87. = 3.141... x d
÷ by value of pi
27.692............. = diameter
Radius is twice the diameter. So, divide diameter by 2 to find the radius.
27.692.....÷ 2 = 13.846...
Thus, radius is 13.8cm
Hope this helps!