Answer:
the line y = x
Step-by-step explanation:
(a, b ) and (b, a ) are reflections of each other in the line y = x.
They are therefore both equidistant from the line y = x
What is the product?
Answer: A
Step-by-step explanation:
When multiplying matrices, find the sum of the product of the terms in the first row of the first matrix with the terms in the first column of the second matrix. Repeat for each row and column.
[tex]\left[\begin{array}{cc}a&c\\b&d\end{array}\right] \times \left[\begin{array}{cc}w&y\\x&z\end{array}\right]=\left[\begin{array}{cc}aw+cx&ay+cz\\bw+dx&by+dz\end{array}\right]\\\\\\\left[\begin{array}{cc}-3&4\\2&-5\end{array}\right]\times \left[\begin{array}{cc}3&-2\\1&0\end{array}\right]\\\\\\=\left[\begin{array}{cc}-3(3)+4(1)&-3(-2)+4(0)\\2(3)-5(1)&2(-2)-5(0)\end{array}\right]\\\\\\=\left[\begin{array}{cc}-5&6\\1&-4\end{array}\right][/tex]
Roberta sold goods costing $35,500, her expenses totaled $2,500 and her freight in totaled $750.
Her company's average stock of goods during the same period was $9,500.
The inventory turnover ratio for Roberta's company is
Answer:
Inventory turnover ratio is 3.74
explanation:
Inventory turnover is a ratio of the number of times a company's inventory is sold and replaced in a given period.
Inventory turn over ratio is calculated as ; Cost of goods sold ÷ Average stock of goods sold
= $35,500 / $9500
= 3.74
HELP PLEASE! A Blue Jay wanted to store some acorns for the winter. If she hides 18 acorns per tree, she will be left with four acorns; if she hides 20 acorns per tree, there will be extra space for an additional four acorns (the number of trees is always the same). How many acorns is the Blue Jay going to store for the winter, and in how many trees?
Answer:
Step-by-step explanation:
Let
T = number of trees
A = number of acorns
Given:
A = 18T + 4 ...........................(1)
A = 20T -4 .........................(2)
Equate A from (1) and (2)
20T-4 = 18T+4
simplify and solve for T
20T - 18T = 4+4
2T = 8
T = 4 trees
A = 18T + 4 = 72+4 = 76 acorns, or
A = 20T - 4 = 80 - 4 = 76 acorns.
You work in a machine design department and need to specify the diameter of a pin that slides back and forth through a hole. The hole diameter is specified as 0.500 inch with a tolerance of 0.010 inch. The maximum pun diameter must be 0.002 inch smaller than the minimum hole diameter. If the pin diameter has a tolerance of 0.010 inch what diameter in inches should you specify for the pin?
Answer:
B. 0.478
Step-by-step explanation:
The diameter of the pin is 0.478 inches as per specification.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that perform arithmetic operation are called arithmetic operators.
+ Addition operation : Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation : Subtracts right hand operand from left hand operand.
for example 4 -2 = 2
The hole diameter is specified as 0.500 inches with a tolerance of 0.010 inches.
The maximum pun diameter must be 0.002 inches smaller than the minimum hole diameter.
Diameter: d = 0.500 inch
Tolerance: t = 0.010 inch
Replacing the values:
⇒ dmax = 0.500 - 0.010 - 0.002 - 0.010
Apply the subtraction operation,
⇒ dmax = 0.478 inch
Hence, the diameter of the pin is 0.478 inches as per specification.
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Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. Find the range, variance, and standard deviation for the sample data. Given that these are the top 10 salaries, do we know anything about the variation of salaries of TV personalities in general?
42 40 39 31 22 18 15 12 11.7 10.5
____________________________________________________________________________
The Range of the sample data is $[ ] million. (Type an integer or a decimal)
The variance of the sample data is [ ]. (Round to three decimal places as needed.)
The standard deviation of the sample data is $[ ] million. (Round to three decimal places as needed)
Is the the standard deviation of the sample a good estimate of the variation of the salaries of the TV personalities in general ?
A. yes, because the standard deviation is an unbiased estimator
B. no, because the sample is not representative of the whole population.
C. no, because there is an outlier in the sample data.
D. yes, because the sample is random.
Answer:
If you do not need that actual numbers, the answer is B.
Step-by-step explanation:
In order to find a fully comprehensive study, you would need many more people than just 10, not to mention these are the top 10 people in the world.
(Brainliest would be much appreciated!)
A bag contains two red marbles, four green ones, one lavender one, four yellows, and six orange marbles. HINT [See Example 7.] How many sets of four marbles include one of each color other than lavender
Answer:
192
Step-by-step explanation:
There are a total of 15 marbles . When the lavender is left out 14 remain.
Using combinations we find that each of the four color marbles can be chosen in the following way.
2C1*4C1*4C1*6C1= 2*4*4*6= 192
We select one of the two red marbles , one of the four green marbles, one of the four yellow marbles, one of the 6 orange marbles leaving the lavender out.. We apply combinations and then multiply to get the answer.
Find two numbers with difference 62 and whose product is a minimum.
Answer:
31 and -31
Step-by-step explanation:
The two numbers with a difference of 62 and whose product is a minimum are; 31 and -31
Let the two numbers be x and y.We are told that their difference is 62.
Thus; x - y = 62 ---(1)
We want their products to be minimum. Thus;f(x,y) = xy
From eq, making y the subject gives us;
y = x - 62
Thus;
f(x) = x(x - 62)
f(x) = x² - 62x
For the product to be minimum, let us find the derivative of f(x) and equate to zero. Thus;f'(x) = 2x - 62
At f'(x) = 0
2x - 62 = 0
2x = 62
x = 62/2
x = 31
Thus;
y = 31 - 62
y = -31
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If mZNOM = 30°, then what is the length of the minor arc
NM?
Answer:
Option (B)
Step-by-step explanation:
To determine the length of arc of a circle we use the formula,
Length of arc = [tex]\frac{\theta}{360}(2\pi r)[/tex]
Where θ = measure of the central angle subtended by the arc
r = radius of the circle
For the circle given in the picture attached,
Length of arc NM = [tex]\frac{30}{360}(2\pi)(2)[/tex]
= [tex]\frac{4\pi }{12}[/tex]
= [tex]\frac{\pi }{3}[/tex]
Therefore, length of [tex]\widehat{NM}=\frac{\pi }{3}[/tex]
Option (B) will be the answer.
Answer: C
Step-by-step explanation:
4#/12 = #
What is the value of Sine theta in the diagram below?
Answer:
C) 24/25
Step-by-step explanation:
did the quiz and got it right
The value of the sine theta in the first quadrant in the diagram given is [tex]\mathbf{\dfrac{24}{25}}[/tex]
What is the trigonometric function in the first quadrant?The explanation of the trigonometric functions (i.e cosine, sine, tangent) in respect of point coordinates on the unit circle informs us of the signs and meanings of the trigonometric functions for each of the four(4) quadrants, depending on the signs of the x, as well as, y coordinates in each quadrant.
In the first quadrant;
cos(θ) > 0, sin(θ) > 0 andtan(θ) > 0Thus, we have a positive x and y-axis.
Taking the forms x and y, i.e. (x, y) = (cos θ, sin θ)
The value of sine theta in [tex]\mathbf{(\dfrac{7}{25}, \dfrac{24}{25} ) = \dfrac{24}{25} }[/tex]
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Jack is doing a test launch of his hovercraft for the upcoming STEM competition.
Answer:
The answer is missing.
I think there is something wrong with the equation on its own
Step-by-step explanation:
Equation for the hovercraft
F(x)= X²+6x+2
Olivia catapult equation
F(x)= √2x
Differential of the both equation will give the velocity at x time
F(x)= X²+6x+2
DF(x)/Dx= 2x +6
F(x)= √2x
F(x)= (2x)^½
DF(x)/Dx= (2x)^-½
So the differential is the velocity of the both equation.
Let's equate both equation to find the value of x at which they have same velocity.
(2x)^-½=- 2x+6
(2x)^-1= (-2x+6)²
(2x)^-1= 4x² -24x +36
0= 8x³ - 48x² +72x -1
The sum of a number and 9 is subtracted from 60. The result is 10. Find the number.
Answer:
Number : 41
Step-by-step explanation:
Say that this number is x. The sum of this number ( x ) and 9 subtracted from 60 will be 10. Therefore we can create the following equation to solve for x,
60 - (x + 9) = 10,
60 - x - 9 = 10,
51 - x = 10,
- x = 10 - 51 = - 41,
x = 41
This number will be 41
Write the equation of the line in point-slope form that passes through (1, -4) and has a slope of 1/4.
Answer:
y + 4 =(1/4)(x - 1)
Step-by-step explanation:
The point slope equation is y - k = m(x - h), where (h, k) is the given point and m is the given slope.
In this particular case we have y + 4 =(1/4)(x - 1)
What is the relationship between angle a and angle b A) Vertical Angles B) Complementary Angles C) Supplementary Angles D) None of the above
Answer:
C. Supplementary
Step-by-step explanation:
Angle a and angle b are on the line CZA.
We can assume that line CZA is a straight line, which is equal to 180 degrees.
Since angle a and b are on the straight line together, they must add to 180 degrees. Therefore, they are supplementary angles.
So, choice C. Supplementary angles is correct.
Find the value of annuity if the periodic deposit is $1500 at 8% compounded semiannually for 22 years
Answer:
The value of annuity is [tex]P_v = \$ 32058[/tex]
Step-by-step explanation:
From the question we are told that
The periodic payment is [tex]P = \$ 1500[/tex]
The interest rate is [tex]r = 8\% = 0.08[/tex]
Frequency at which it occurs in a year is n = 2 (semi-annually )
The number of years is [tex]t = 22 \ years[/tex]
The value of the annuity is mathematically represented as
[tex]P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ][/tex](reference EDUCBA website)
substituting values
[tex]P_v = 1500 * [1 - (1 + \frac{0.08}{2} )^{-22 * 2} ] * [\frac{(1 + \frac{0.08}{2} )}{ \frac{0.08}{2} } ][/tex]
[tex]P_v = 1500 * [1 - (1.04 )^{-44} ] * [\frac{(1.04 )}{0.04} ][/tex]
[tex]P_v = 1500 * [1 - 0.178 ] * [\frac{(1.04 )}{0.04} ][/tex]
[tex]P_v = \$ 32058[/tex]
A building has eight levels above ground and one level below ground. The height of each level from floor to ceiling is feet. What is the net change in elevation going from the floor of the underground level to the ceiling of the fourth level above ground? Assume the floor at ground level is at an elevation of zero feet.
Answer:
72.5 feet
Step-by-step explanation:
The height of each level from floor to ceiling is 14 1/2 feet.
We want to find the net change in elevation going from the floor of the underground level to the ceiling of the 4th level above ground.
In other words, the change in elevation in going 5 floors up.
Each level has a height of 14 1/2 feet (29/2 feet).
Therefore, the height of the fourth level above ground from the underground level will be 5 times the height of one level:
h = 5 * 29/2 = 72.5 feet
The net change in elevation from the floor of the underground level to the 4th level above ground is:
ΔE = [tex]h_4 - h_0[/tex]
[tex]h_0 = 0 feet\\\\h_4 = 72.5 feet[/tex]
Therefore:
ΔE = 72.5 - 0 = 72.5 feet
Answer:
72.5
Step-by-step explanation:
If John has pairs of red, orange, yellow, blue and green socks, how many can he wear them in over 5 days, repetition is allowed because hog is alright with wearing dirty socks. A)5! B)25 C)5^5 D)125
Answer:
Total ways = 5×5×5×5×5
Total ways = 5^5
Total ways = 3125
Therefore, the correct option is C) 5^5
Step-by-step explanation:
John has pairs of red, orange, yellow, blue and green socks.
Which means that John has 5 different colors pairs of socks.
We are asked to find out in how many ways can he wear them over 5 days.
1st Day:
On the first day John has 5 ways to choose from.
2nd Day:
On the second day John has 5×5 ways to choose from.
(Since repetition is allowed)
3rd Day:
On the third day John has 5×5×5 ways to choose from.
4th Day:
On the fourth day John has 5×5×5×5 ways to choose from.
5th Day:
On the fifth day John has 5×5×5×5×5 ways to choose from.
Total ways = 5×5×5×5×5
Total ways = 5^5
Total ways = 3125
Therefore, the correct option is C) 5^5
I need help for this problem!
Answer:
[tex] a = 2.7 [/tex]
Step-by-step explanation:
Distributive property can be used to solve the equation, by multiplying [tex] \frac{2}{3} [/tex] with [tex] 6a, [/tex] and [tex] 9 [/tex]
Thus,
[tex] (\frac{2}{3}*6a) + (\frac{2}{3}*9) = 16.8 [/tex]
[tex] 2*2a + 2*3 = 16.8 [/tex]
[tex] 4a + 6 = 16.8 [/tex]
Subtract 6 from both sides.
[tex] 4a + 6 - 6 = 16.8 - 6 [/tex]
[tex] 4a = 10.8 [/tex]
Divide both sides by 4 to solve for a
[tex] \frac{4a}{4} = \frac{10.8}{4} [/tex]
[tex] a = 2.7 [/tex]
The surface area of a given cone is 1,885.7143 square inches. What is the slang height?
This question is not complete. This is because it lacks the appropriate diagram containing necessary information to solve this question.
Please find attached the appropriate diagram to solve for this question
Complete Question :
The surface area of a given cone is 1,885.7143 square inches. What is the slant height?
Answer:
25 inches
Step-by-step explanation:
In the diagram, we are given the following information
Height of the cone = 20 inches
Radius of the cone = 15 inches.
The formula for the slant height of a cone represented by l =
l² = r² + h²
l = √(r² + h²)
l = √(15² + 20²)
l = √(225 + 400)
l = √625
l = 25 inches
Therefore, the slant height of this cone = 25 inches
Consider a triangle ABC like the one below. Suppose that B=36°, C= 62°, and b= 40. (The figure is not drawn to scale.) Solve the triangle.
Round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
Answer:
A=82°
a= 67.4
c = 60.1
Step-by-step explanation:
For A
A+B+C =180°
A= 180-(B+C)
A= 180-(36+62)
A= 189-(98)
A= 82°
For a
a/sinA= b/sinB
a/sin82= 40/sin36
a= (40*sin82)/sin36
a=( 40*0.9903)/0.5878
a=67.39
Approximately = 67.4
For c
c/sinC= b/sinB
c= (sinC*b)/sinB
c= (sin62*40)/sin36
c =(0.8829*40)/0.5878
c = 60.08
Approximately = 60.1
What is the equation of the circle show in the image?
Given the radius of a circle is 7 cm, what is the circumference?
Answer:
14π or 43.96
Step-by-step explanation:
C = 2πr and we know that r = 7 so C = 14π or 43.96.
Select the correct answer from each drop down menu.
The slope of diagonal OA is
A) 4/3
B) 3/4
C) 1
,and it’s equation is
A) 4x-y=0
B) x-3y=0
C) 4x-3y=0
Answer:
(A) [tex]\text{The slope of OA is }\dfrac{4}{3}[/tex]
(C) It’s equation is 4x-3y=0.
Step-by-step explanation:
Point O is at (0,0)
Point A is at (3,4)
[tex]\text{Slope of OA}=\dfrac{4-0}{3-0} \\m=\dfrac{4}{3}[/tex]
The equation of a straight line is in the form: y=mx+b
The y-intercept of the line OA=0
Therefore, we have:
[tex]y=\dfrac{4}{3}x+0\\3y=4x+0\\$Subtract 3y from both sides$\\4x-3y=0[/tex]
The equation of the line is: 4x-3y=0
the solution of the equation 0=4+4(m+1) is
Answer:
[tex]\boxed{m = -2}[/tex]
Step-by-step explanation:
[tex]0 = 4+4(m+1)[/tex]
Resolving Parenthesis
[tex]0 = 4+4m + 4[/tex]
[tex]0 = 4m+8[/tex]
Subtracting 8 to both sides
[tex]-8 = 4m[/tex]
[tex]4m = -8[/tex]
Dividing both sides by 4
m = -8/4
m = -2
Step-by-step explanation:
4+4m+4= 0
4m+8=0
4m=-8
m= -8/4=-2
Tasha wants to measure the height of a tree that grows at an angle of 85° with respect to the ground.
When she is 80 feet away from the base of the tree she looks up. The angle from the ground to the top of
the tree is 25°. Approximately, how tall is the tree?
Answer: 35.9
Step-by-step explanation:
The tree is approximately 35.979 feet tall, computed using the sine rule.
What is the sine rule?The sine rule in a triangle can be shown as this.
A triangle ABC, with the values of the side BC = a, CA = b, and AB = b, follows the rule by:
(Sin A)/a = (sin B)/b = (sin C)/c.
How to solve the given question?In the question, we are informed about Tasha who is willing to measure the height of a tree, which grows at an angle of 85° with respect to the ground. Also, we are informed that when Tasha is 80 feet away from the base of the tree, then the angle from the ground to the top of the tree is 25°.
We are asked to find the height of the tree.
We first draw a triangle using the given details, AB being the tree, and C being the point where Tasha is.
We know ∠A = 180° - (∠B + ∠C) {By angle sum property of triangles)
or, ∠A = 180° - (85° + 25°) = 180° - 110° = 70°.
Now, by sine rule, we can say that:
(Sin A)/a = (sin B)/b = (sin C)/c.
or, (Sin 70°)/80 = (sin 85°)/b = (sin 25°)/c,
or, 0.93969262078/80 = 0.42261826174/c {We ignored the middle term as we only need the height of the tree, that is, c}
or, c = 0.42261826174*80/0.93969262078/80
or, c = 35.9792768309.
Therefore, the tree is approximately 35.979 feet tall, computed using the sine rule.
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The function y=−16x2+v0x models the height of a football in feet x seconds after a player kicks it. In the equation of the function, v0 is the ball's initial velocity in feet per second. The ball hits the ground 2 seconds after the player kicks it.
What is the value of v0?
Answer:
[tex]\large \boxed{\sf \ \ v_0=32 \ \ }[/tex]
Step-by-step explanation:
Hello,
The equation is
[tex]y=f(x)=-16x^2+v_0 \cdot x[/tex]
The ball hits the ground 2 seconds after the player kicks it, it means that f(2)=0.
We need to find [tex]v_0[/tex] such that f(2)=0.
[tex]f(2)=-16\cdot 2^2+v_0 \cdot 2=-64+2v_0=0\\\\\text{*** add 64 to both sides ***}\\\\2v_0=64\\\\\text{*** divide by 2 both sides ***} \\\\v_0=\dfrac{64}{2}=32[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
v0 = 32 ft/s
Step-by-step explanation:
i would like some help thank you :)
Answer:
[tex]\angle AE = 32^{\circ}[/tex]
[tex]\angle EAD = 212^{\circ}[/tex]
[tex]\angle BE = 133^{\circ}[/tex]
[tex]\angle BCE = 227^{\circ}[/tex]
[tex]\angle AED = 180^{\circ}[/tex]
[tex]\angle BD = 79^{\circ}[/tex]
Step-by-step explanation:
The central angle of a circle is equal to 360º, whose formula in this case is:
[tex]\angle AB + \angle BC + \angle CD + \angle DE + \angle EA = 360^{\circ}[/tex]
In addition, the following conditions are known from figure:
[tex]\angle BC = 47^{\circ}[/tex], [tex]\angle DE = 148^{\circ}[/tex]
[tex]\angle DE + \angle EA = 180^{\circ}[/tex]
[tex]\angle CD + \angle DE = 180^{\circ}[/tex]
[tex]\angle AB + \angle BC + \angle CD = 180^{\circ}[/tex]
Now, the system of equations is now solved:
[tex]\angle EA = 180^{\circ}-\angle DE[/tex]
[tex]\angle EA = 180^{\circ}-148^{\circ}[/tex]
[tex]\angle EA = 32^{\circ}[/tex]
[tex]\angle CD = 180^{\circ}-\angle DE[/tex]
[tex]\angle CD = 180^{\circ}-148^{\circ}[/tex]
[tex]\angle CD = 32^{\circ}[/tex]
[tex]\angle AB = 180^{\circ} - \angle BC - \angle CD[/tex]
[tex]\angle AB = 180^{\circ}-47^{\circ}-32^{\circ}[/tex]
[tex]\angle AB = 101^{\circ}[/tex]
The answers are described herein:
[tex]\angle AE = 32^{\circ}[/tex]
[tex]\angle EAD = 212^{\circ}[/tex]
[tex]\angle BE = 133^{\circ}[/tex]
[tex]\angle BCE = 227^{\circ}[/tex]
[tex]\angle AED = 180^{\circ}[/tex]
[tex]\angle BD = 79^{\circ}[/tex]
Amber says that the data set is left-skewed because the box is farther to the left on the number line. (A) Is Amber correct? (B) Explain your reasoning.
Before hosting their annual Chess Tournament and Spelling Bee, a school received 7 boxes of honorary medals: one medal for every participant. After the Chess Tournament, two boxes were empty and the rest were still closed. After the Spelling Bee, which had twice as many participants, there were 72 medals left. How many people competed in the Chess Tournament?
Answer:
144 people competed in the Chess Tournament
Step-by-step explanation:
So as you can see, after the Chess Tournament took place, two boxes were empty, the rest closed. That would mean that there were 2 boxes of medals that were given out to honor the participants in the chess tournament. The spelling bee had twice as many participants, and hence used 2 [tex]*[/tex] 2 = 4 boxes. The remaining box had to have 72 medals in it, as it was the remaining amount of medals.
After the Chess Tournament, 2 boxes were given out, and we can assume they contained 72 medals in them. Therefore, the number of medals given after the chess tournament would be 2 [tex]*[/tex] 71 = 144 medals. Each medal corresponds to a participant, so the number of chess tournament participants would also be 144, 144 participants.
Which of the binomials below is a factor of this trinomial?
x2 - 5x+ 4
O A. X-1
O B. x2 + 4
C. X+4
D. X + 1
Answer:
A
Step-by-step explanation:
To factor x² - 5x + 4, we need to find 2 numbers that have a sum of -5 and product of 4; these 2 numbers are -1 and -4 so the factored version is (x - 1)(x - 4). Since x - 4 is not an answer choice but x - 1 is, the answer is A.
The area of each square below is 1 square unit. How can we calculate the area of the striped region? A: 7/5 x 1/2 B: 6/12 x 2/10 C: 7/5 x 2/10
Answer:
wrong thing
Step-by-step explanation:
13 arent shaded of the 20 units
7/20 are shaded, 7X1=7, 2X5=10