Answer:
In bold below.
Step-by-step explanation:
(a) The largest angle is opposite the largest side.
So by the Cosine Rule:
8^2 = 4^2 + 6^2 - 2*4*6 cos x
cos x = (8^2 - 4^2 - 6^2) / (-2*4* 6)
= -0.25.
x = 104.48 degrees.
(b) Area of the triangle = 1/2 * 4 * 6 sin 104.48
= 11.62
= 3 √15.
(c) The shortest altitude will have the longest sides as the base.
Area = 1/2 * altitude * base
3√15 = 1/2 * 8 * a
a = 3√15 / 4 cm
= 0.75√15 cm.
The cosine of the largest angle is 104.48 degrees
The area of the triangle is 3√15cm² is 3 √15
The length of the shortest altitude of the triangle is 0.75√15 cm.
A triangle can be defined as a figure that has three lines. It can be of various dimensions it can a scale as Pythagoras or an isosceles triangle. They all have different properties.
(a)
With the help of the Cosine Rule:
[tex]8^2[/tex] = [tex]4^2 + 6^2 - 2 \times 4\times6 cos x[/tex]
cos x = [tex](8^2 - 4^2 - 6^2) / (-2 \times 4 \times 6)[/tex])
= -0.25.
x = 104.48 degrees.
(b)
Area of the triangle
=[tex]1/2 \times 4 \times 6 sin 104.48[/tex]
= 11.62
= 3 √15.
(c)
Area =[tex]1/2 \times altitude \times base[/tex]
3√15 = 1/2 * 8 * a
a = 3√15 / 4 cm
= 0.75√15 cm.
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True or False: Results that are practically significant will always be statistically significant.
Answer:
This is false
Step-by-step explanation:
Because we have to understand that some times sample mean may be very high that is they may be practically significant but are not statistically significant because the calculated p-value is not less than alpha value which could only mean that they could occur as a result of mere chance.
is 0.007x10 equivalent to 0.07
Answer: yes.
Step-by-step explanation:
adding 10 is moving the decimal point once to the right, so yes.
move the decimal point in 0.007 once to the right (multiply it by 10) and you get 0.07
Answer:
Yes
Step-by-step explanation:
Multiply 0.007 by 10 by moving the decimal over to the right one place. It should now look this this: 0.07slove it this question
Answer:
a = 60°
Step-by-step explanation:
Formula used:
[tex] \red{\boxed {\bold {\tan \: \theta = \cot \: (90\degree - \theta)}}} [/tex]
[tex] \tan \: 30 \degree = \cot \: a \\ \cot \: (90 \degree - 30 \degree) = \cot \: a \\ cot \: 60 \degree = \cot \: a \\ 60 \degree = a \\ \huge \red{ \boxed{ a = 60 \degree}}[/tex]
Classify the two given samples as independent or dependent. Sample 1: Pre-training blood pressure of 17 people Sample 2: Post-training blood pressure of 17 people a. dependent b. independent
Answer:
Sample 1 : independent
Sample 2 : dependent
Step-by-step explanation:
From the question we are told that
The given date is
Sample 1: Pre-training blood pressure of 17 people
Sample 2: Post-training blood pressure of 17 people
Now Sample 1 is independent because the Pre-training blood pressure of 17 people does not depend of Post-training blood pressure of 17 people
While
Sample 2 is dependent because the Post-training blood pressure of 17 people is dependent on the Pre-training blood pressure of 17 people
Which statement is true? (Please help)
Answer:
Option (2)
Step-by-step explanation:
From the picture attached,
Angle between HB and FG = 90°
Therefore, HB and FG are perpendicular segments.
HB ⊥ FG
Similarly, angle between HB and AC = 90°
Therefore, both the segments HB and AC will be perpendicular.
HB ⊥ AC
Since FG and AC are both perpendicular to HB.
Therefore, FG║AC.
Option (2) will be the correct option.
Tomas works as an underwater photographer. He starts at a position that is 17 feet below sea level. He rises 7 feet, then descends 13 feet to take a photo of a coral reef. Enter an expression to find his position relative to sea level when he took the photo and then evaluate the expression.
Answer:
(-17+7)-13 or -17-13+7
Step-by-step explanation:
Answer:
Step-by-step explanation: -17+7=10-13=-2
Evaluate the expression when a = -6 and y=2 . a-6y
Answer:
-18
Step-by-step explanation:
So we have the expression:
[tex]a-6y[/tex]
And we want to evaluate it when y=2 and a=-6.
Substitute in these values:
[tex]=(-6)-6(2)[/tex]
Multiply:
[tex]=(-6)-12[/tex]
Subtract:
[tex]=-18[/tex]
Answer:
-18
Step-by-step explanation:
We are given the expression:
[tex]a-6y[/tex]
and asked to evaluate when a= -6 and y=2.
Therefore, we must substitute -6 in for a and 2 in for y.
[tex]a-6y , a=-6, y=2[/tex]
[tex](-6)-6(2)[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Addition, and Subtraction.
Multiply 6 and 2.
[tex](-6)-(6*2)[/tex]
[tex](-6)-(12)[/tex]
[tex](-6)-12[/tex]
Subtract 12 from -6.
[tex](-6-12)[/tex]
[tex]-18[/tex]
The expression a-6y when evaluated for a=-6 and y=2 is equal to -18.
insert two fractions between 3/5 and 4/7
(1) 10/12, 5/9 (2) 11/15, 8/9 (3) 10/17, 7/12 (4) 18/10,6/5
The ratio of boys to girls in Mrs. Johnson's class is 4 to 5. There are 10 girls in the class. What is the total number of students in Mrs. Johnson's class?
Answer:
i think it would be 18 kids in the class
Step-by-step explanation:
since for every 4 boys there are 5 girls and so it means
so for every 10 girls there would be 8 boys
what is a product concept?
Answer:
so just be you
Step-by-step explanation:
A product concept statement, sometimes referred to as just a "concept statement" represents the vision that a business owner and his design team has for a product or service. It describes the product or service, explains its purpose and considers the consumer demographics that the product is market toward.
First answer gets Brainlyist
Question 61 point
5. Of the 30 girls who tried out for the lacrosse team
at Euclid Middle School, 12 were selected. Of the
40 boys who tried out, 16 were selected. Are the ratios
of the number of students on the team to the number of
students trying out the same for both boys and girls?
How do you know?
I
what type of shape is a square
Answer:
A square is a closed, two dimensional shape with 4 equal sides.
It is also a quadrilateral.
Step-by-step explanation:
none :)
A lumber company is making boards that are 2599.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A sample of 23 is made, and it is found that they have a mean of 2600.3 millimeters with a standard deviation of 13.0. A level of significance of 0.05 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the boards are either too long or too short?
Answer:
There is no sufficient evidence to support the claim that the boards are either too long or too short
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 2599.0[/tex]
The sample size is [tex]n = 23[/tex]
The sample mean is [tex]\= x = 2600.3 \ mm[/tex]
The standard deviation is [tex]\sigma = 13.0[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 2599.0[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 2599.0[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma}{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 2600.3 - 2599.0 }{ \frac{13}{ \sqrt{ 23} } }[/tex]
=> [tex]t = 0.3689[/tex]
Now from the normal distribution table the critical value of [tex]\alpha[/tex] is
[tex]Z_{\alpha } = 1.645[/tex]
Hence from the evaluated and obtained value we see that
[tex]t < Z_{\alpha }[/tex]
Hence we fail to reject the null hypothesis
Thus we can conclude that there is no sufficient evidence to support the claim that the boards are either too long or too short
Write an expression to represent the total cost of paint at a rate of $5.75 per ft.? to paint a triangular-shaped mural where the base of the triangle is 22 feet longer than the height
Answer:
C($)= (x²/2 +11x)5.75
Step-by-step explanation:
Let's assume the height= x
The base= x+22
Area= 1/2(base*height).
Area= 1/2((x+22)(x))
Area= x²/2 +11x
Cost per ft= $5.75
Cost for painting the triangular mural C
C($)= (x²/2 +11x)5.75
Find the area of the rectangle . (9,-1), (-1,7), (-5,2), (5,-6)
Answer:
(5,-6)
Step-by-step explanation:
Answer: 82 sq. units .
Step-by-step explanation:
Solve for U. 4(3-U)+U= 22+2U
Step-by-step explanation:
4(3-U)+U = 22+2U
12-4U+U = 22 + 2U
12-5U= 22+2U
10=3U
U = 10/3
U= 3.3
Find a 3-by-3 magic square using the numbers 6, 8, 10, 13, 15, 17, 20, 22, and 24.
Fill in the magic square.
The required magic square using the numbers 6, 8, 10, 13, 15, 17, 20, 22, and 24 is | 6 | 8 | 10 |
| 13 | 15 | 17 |
| 20 | 22 | 24 |.
What is a magic square?A magic square is a square grid of numbers, typically integers, where the numbers in each row, column, and diagonal add up to the same constant value.
Here,
To create a magic square using the numbers 6, 8, 10, 13, 15, 17, 20, 22, and 24, we can follow these steps,
Start by placing the number 15 in the center square of the grid.
Place the number 6 in one corner of the grid. We'll choose the top left corner for this example.
Place the number 24 in the opposite corner. We'll choose the bottom right corner for this example.
Place the remaining numbers in the empty squares of the grid, following these rules:
a. If a square is already occupied, move to the next square in the same direction.
b. If you reach the edge of the grid, wrap around to the other side.
c. If you reach a square that is diagonally adjacent to a previously filled square, move to the next empty square in a clockwise direction.
Using these rules, we can fill in the rest of the grid as follows:
| 6 | 8 | 10 |
| 13 | 15 | 17 |
| 20 | 22 | 24 |
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Which algebraic expression is a polynomial
A checking account has a balance of $350.00. A customer makes two withdrawals, one $50.0 more than the other. Then he makes a $75.00 deposit.
Answer: $25
Step-by-step explanation:
Use the equation to answer the questions. Round both answers to nearest whole number. Y=51.75−1.25X If Y equals 4, what is X?
Answer:
38.2, or 38 1/2
Step-by-step explanation:
Steps for Solving Linear Equation:
4=51.75−1.25x
Swap sides so that all variable terms are on the left hand side.
51.75−1.25x=4
Subtract 51.75 from both sides.
−1.25x=4−51.75
Subtract 51.75 from 4 to get −47.75.
−1.25x=−47.75
Divide both sides by −1.25.
x=−1.25−47.75
Expand −1.25−47.75≈38.2 by multiplying both numerator and the denominator by 100.
x=−125−4775
Reduce the fraction −125−4775≈38.2 to lowest terms by extracting and canceling out −25.
x=5191
The length of a rectangle is 3 units more than the width. Let x = the width.Then ? = the length.
Answer:
Length = X + 3
Step-by-step explanation:
Examples for the length width relationship would go as follows:
Width Length
1 4
2 5
3 6
4 7
Hope this helps!
-TheBusinessMan
Answer:
Length = x + 3
Step-by-step explanation:
Width = x
Length = 3 + Width
So, Length = 3 + x
So, if Width as a number, then Length will be 3 more than that number.
Hazel graphs a point on a coordinate plane. The point is located 4 units from the x-axis. Which order pair could describe the point that Hazel graphs.
A. (9,5)
B. (3,4)
C. (2,2)
D. (4,1)
Answer: B
Step-by-step explanation: (3, 4) is 4 units above the x-axis
please help i can’t figure this out
7(4+t) - 5(t+1) =
distribute the [tex]7[/tex] and [tex]5[/tex]:
[tex]7(4+t)-5(t+1)=\\28+7t -5t -5[/tex](collect like-terms)
[tex]28-5 +7t-5t=\\23+2t[/tex]
[tex]23+2t[/tex] or [tex]2t+23[/tex] is your answer. hope this helps <3
What is the equation of the line that passes through the point (-4, -3) and has a
slope of 3/4
Answer:
y=3/4x
it passes through (-4,-3) on its own
Can someone help me with this?
Answer:
rational, Natural, Integer, whole
Step-by-step explanation:
remember your perfect squares
the sqrt of 25 is a perfect square
sqrt of 25 is 5
5 is all except irrational
Solve the following System of Three Equations: x−3y+z=−15
2x+y−z=−2
x+y+2z=1
Answer:
x = -3 , y = 4 , z = 0
Step-by-step explanation:
Solve the following system:
{x - 3 y + z = -15
2 x + y - z = -2
x + y + 2 z = 1
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for z:
{x - 3 y + z = -15
2 x + y - z = -2
x + y + 2 z = 1
Hint: | Solve for z.
Subtract x - 3 y from both sides:
{z = 3 y + (-x - 15)
2 x + y - z = -2
x + y + 2 z = 1
Hint: | Perform a substitution.
Substitute z = -15 - x + 3 y into the second and third equations:
{z = -15 - x + 3 y
15 + 3 x - 2 y = -2
x + y + 2 (-15 - x + 3 y) = 1
Hint: | Expand the left hand side of the equation x + y + 2 (-15 - x + 3 y) = 1.
x + y + 2 (-15 - x + 3 y) = x + y + (-30 - 2 x + 6 y) = -30 - x + 7 y:
{z = -15 - x + 3 y
15 + 3 x - 2 y = -2
-30 - x + 7 y = 1
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for x:
{z = -15 - x + 3 y
15 + 3 x - 2 y = -2
-30 - x + 7 y = 1
Hint: | Isolate terms with x to the left hand side.
Subtract 15 - 2 y from both sides:
{z = -15 - x + 3 y
3 x = 2 y - 17
-30 - x + 7 y = 1
Hint: | Solve for x.
Divide both sides by 3:
{z = -15 - x + 3 y
x = (2 y)/3 - 17/3
-30 - x + 7 y = 1
Hint: | Perform a substitution.
Substitute x = (2 y)/3 - 17/3 into the third equation:
{z = -15 - x + 3 y
x = (2 y)/3 - 17/3
(19 y)/3 - 73/3 = 1
Hint: | Choose an equation and a variable to solve for.
In the third equation, look to solve for y:
{z = -15 - x + 3 y
x = (2 y)/3 - 17/3
(19 y)/3 - 73/3 = 1
Hint: | Isolate terms with y to the left hand side.
Add 73/3 to both sides:
{z = -15 - x + 3 y
x = (2 y)/3 - 17/3
(19 y)/3 = 76/3
Hint: | Solve for y.
Multiply both sides by 3/19:
{z = -15 - x + 3 y
x = (2 y)/3 - 17/3
y = 4
Hint: | Perform a back substitution.
Substitute y = 4 into the first and second equations:
{z = -x - 3
x = -3
y = 4
Hint: | Perform a back substitution.
Substitute x = -3 into the first equation:
{z = 0
x = -3
y = 4
Hint: | Sort results.
Collect results in alphabetical order:
Answer: {x = -3 , y = 4 , z = 0
PLEASE HELP QUICKLY AS POSSIBLE THANK YOU!!!!!
Answer: 7 pt
Step-by-step explanation:
1 U.S pt is 2 cups
take 14 divided by 2
= 7
The Graduate Record Exam (GRE) has a combined verbal and quantitative mean of 1000 and a standard deviation of 200. Scores range from 200 to 1600 and are approximately normally distributed. For each of the following problems: (a) Indicate the percentage or score called for by the problem.(b) draw a rough sketch, darkening in the portion of the curve that relates to the answer, and1) What percentage of the persons who take the test score above 1300?2) What percentage score above 800?3) What percentage score below 1200?4) Above what score do 20% of the test-takers score?5) Above what score do 30% of the test-takers score?
Answer:
1.)6.68% ; 2)84.13% ; 3)84.13% ; 4)1168 ; 5)1105
Step-by-step explanation:
Given a normal distribution with:
Mean (m) = 1000
Standard deviation (sd) = 200
1) What percentage of the persons who take the test score above 1300?
X = 1300
Zscore = (x - m) / sd
Zscore = (1300 - 1000) / 200 = 300/200 = 1.5
P(z > 1.5) = 1 - p(z < 1.5) ;
From the z distribution table:
p(z < 1.5) = 0.9332 ; 1 - 0.9332 = 0.0668 = 6.68%
2) What percentage score above 800?
X = 800
Zscore = (x - m) / sd
Zscore = (800 - 1000) / 200 = - 200/200 = - 1
P(z > - 1) = 1 - p(z < - 1) ;
From the z distribution table:
p(z < - 1) = 0.1587 ; 1 - 0.1587 = 0.8413 = 84.13%
3) What percentage score below 1200?
X = 1200
Zscore = (x - m) / sd
Zscore = (1200 - 1000) / 200 = 200/200 = 1
p(z < 1)
From the z distribution table:
p(z < 1) = 0.8413 = 84.13%
Above what score do 20% of the test takers score?
P(z > Zscore) = 0.2 = P(z > Zscore) = 1 - 0.2 = 0.8
P(z < Zscore) = 0.8
0.8 is closest to a Zscore of 0.84
From the formula:
Zscore = (x - m) / sd
0.84 = (x - 1000) / 200
168 = x - 1000
x = 168 + 1000 = 1168
Above what score do 30% of the test takers score?
P(z > Zscore) = 0.3 = P(z > Zscore) = 1 - 0.3 = 0.7
P(z < Zscore) = 0.7
0.8 is closest to a Zscore of 0.525
From the formula:
Zscore = (x - m) / sd
0.525 = (x - 1000) / 200
105 = x - 1000
x = 105 + 1000 = 1105
Which statement about correlation is FALSE?
A) Correlation is a quantitative measure of the strength of a linear association between two variables.
B) Correlation is a quantitative measure of the strength of a non-linear association between two variables.
C) A correlation of -1 or 1 corresponds to a perfectly linear relationship.
D) Correlation is measured by r, the correlation coefficient which has a value between -1 and 1.
Correlation is a quantitative measure of the strength of a non-linear association between two variables.
Statement B is false because the r value measures the linear association between two variables. In other words, it tells us how good a linear fit we have with a scatterplot of data. So this is why statement A is true.
As r gets closer to +1, then we have a stronger positive linear correlation. If r = 1 exactly, then all points fall on the same straight line with positive slope (the slope isn't necessarily m = 1). Conversely, if r = -1, then the points fall on the same straight line with negative slope (not necessarily m = -1). As r gets closer to r = 0, the strength of the linear relationship weakens. All of this points to statements A, C, and D to be true statements.
Answer:
Correlation is a quantitative measure of the strength of a non-linear association between two variables.
Step-by-step explanation:
Correlation specifically measures the strength and direction of a linear association between two variables. So we can't use it for all variables or for non-linear associations.