Let:
[tex]y=ax[/tex]The equation which represents a direct variation. where a is the constant of proportionality.
[tex]\begin{gathered} x=3,y=6 \\ 6=3a \\ a=\frac{6}{3} \\ a=2 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} x=k,y=4 \\ 4=2k \\ solve_{\text{ }}for_{\text{ }}k\colon_{} \\ k=\frac{4}{2} \\ k=2 \end{gathered}[/tex]Which pairs of non- overlapping angles share a ray to make a right angle? Select all that apply.
From the figure the pairs of angles that share a ray to make a right angle are:
[tex]\begin{gathered} \measuredangle EGK\text{ and }\measuredangle KGF \\ \measuredangle\text{FGJ and }\measuredangle JGH \end{gathered}[/tex]Answer: Option 1 and Option 4.
draw examples of each figure: - 2 perpendicular lines-AB AC ray on same line-EW intersecting with EMI'll upload picture
Part c
N 11
2 perpendicular lines
see the figure below
N 12
see the figure below
N 13
see the figure below
A friend lends you $260, which you agree to repay with 3% interest.How much will you have to repay?How much of that was interest?
To answer this question we will use the following formula to compute the x% of y:
[tex]y\times\frac{x}{100}.[/tex]Since you have to repay with 3% interest, then you have to pay 103% of the original amount.
The 103% of 260 is:
[tex]260\times\frac{103}{100}=267.80.[/tex]Now, notice that the interest is the difference between the original amount and the above result:
[tex]I=267.80-260=7.80.[/tex]Answer:
How much will you have to repay? $267.80.
How much of that was of interest? $7.80.
A . Explain the meaning of the statement f (7) = 5. o The amount of garbage produced per week by a city with population 7,000 is 5 tons. o The amount of garbage produced per week by a city with population 5,000 is 7 tons. o The amount of garbage produced per week by a city with population 70,000 is 5 tons.o The amount of garbage produced per week by a city with population 5 is 7 tons.o The amount of garbage produced per week by a city with population 7 is 5 tons.
It will be as follows:
*The amount of garbage produced per week by a city with a population of 7000 is 5 tons. [Assuming IS ton that would be 5000 Kg, so the relationship would be linear, ie: for each 1000 population, there will be produced 1 ton (1000Kg)]
Rochelle needs to pack a picture frame that measures 7 3/8 inches on each side will it be into a box that measures 7.4 inches on each side
A picture frame that is 7 3/8 inches wide on each side needs to be packed into a box that is 7.4 inches wide on each side. It would not consequently fit.
Given that,
A picture frame that is 7 3/8 inches wide on each side needs to be packed into a box that is 7.4 inches wide on each side.
Picture frame length is 7 3/8, or 7.4 inches.
Box length is 7.4 inches.
Therefore, it is clear from the about that the box's length is shorter than the picture frame's length.
It would not consequently fit.
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A microwave company claims that their microwaves can pop popcorn in under 2.25 minutes. After 134 randomly chosen microwaves were sampled, it was found that the mean time to pop popcorn was 2.5 minutes, with a standard deviation of .25 minutes. Using the information provided, determine if this claim should be rejected?A. Reject the null hypothesis. There is not enough evidence to oppose the microwave company's claim.B. Reject the null hypothesis. There is enough evidence to oppose the microwave company's claim.C. Fail to reject the null hypothesis. There is not enough evidence to oppose the microwave company's claim.D. Fail to reject the null hypothesis. There is enough evidence to oppose the microwave company's claim.
ANSWER
A. Reject the null hypothesis. There is not enough evidence to oppose the microwave company's claim.
EXPLANATION
The claim is that the microwave can make popcorn in under 2.5 minutes. Hence, the statistical hypotheses are:
[tex]\begin{gathered} H_0\colon\mu\ge2.25 \\ H_1\colon\mu<2.25 \end{gathered}[/tex]where H0 = null hypothesis
H1 = the hypothesis we are interested in proving
The level of significance of the test is not given, hence, we can assume that the level of significance of the test is 5%:
[tex]\alpha=5\%=0.05[/tex]Since the sample size is n = 134, we can use the approximation to the standard normal distribution to calculate the test statistic:
[tex]z=\frac{\bar{x}-\mu}{\frac{S}{\sqrt[]{n}}}[/tex]For the given sample:
[tex]\begin{gathered} n=134 \\ \bar{x}=2.5\text{ min} \\ S=0.25 \\ \mu=2.25\text{ min} \end{gathered}[/tex]Hence, we have that:
[tex]\begin{gathered} z=\frac{2.5-2.25}{\frac{0.25}{\sqrt[]{134}}} \\ z=\frac{0.25}{\frac{0.25}{11.5758}} \\ z=0.25\cdot\frac{11.5758}{0.25} \\ z=11.5758 \end{gathered}[/tex]Now, we have to find the p-value.
If the p-value is greater than the significance level, the decision is to not reject the null hypothesis.
If the p-value is less than the significance level, the decision is to reject the null hypothesis.
For any z-score value greater than 3, the accumulated probability is 0.99999 and for any value below -3, the accumulated probability is 0.
We have that the z-score is 11.5758. This means that:
[tex]\begin{gathered} P(z>11.58)=1-P(z<11.57)=1-0.99999 \\ \Rightarrow P(z>11.58)=0.00001 \end{gathered}[/tex]As we can see, the p-value is less than the significance level, so the decision is to reject the null hypothesis.
This means that the alternative hypothesis:
[tex]H_1\colon\mu<2.25[/tex]is right (or stays) and so, the claim of the company is right.
Hence, the correct answer is option A.
please help me answer the question in the image. thank you for any help and explanations you can give me!
We can solve this type of question using trigonometric functions. Here, we use sine of the angle of take-off with the horizontal runway.
[tex]\begin{gathered} \sin 10^o=\frac{500}{c} \\ c=\frac{500}{\sin 10^o} \\ c=\frac{500}{0.1736} \\ c=2880.18 \end{gathered}[/tex]Thus, the distance that the plane has traveled is equal to 2880 ft.
Determine whether or not the following correspondences specify a function, and explain your reasoning in writing
Recall that a relation is a function if for every value on the domain there is only one value on the range.
(a) Notice that for every value on the domain, there is only one value on the range:
For the value 0 in the domain, there is the value 5 in the range.
For the value 1 in the domain, there is the value 6 in the range.
For the value 2 in the domain, there is the value 7 in the range.
For the value 3 in the domain, there is the value 7 in the range.
Therefore the relation represented by the given graph in a) is a function.
(b) Notice that for the value 3 in the domain there are two values in the range, 6 and 7, therefore, the relation represented by the graph in b) is not a function.
Answer:
(a) Function.
(b) Not a function.
The radius of a circle is 9 inches. What is the length of a 45° arc?
SOLUTION:
Step 1:
In this question, we are given the following:
The radius of a circle is 9 inches.
What is the length of a 45° arc?
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Arc\text{ length = }\frac{\theta}{360^0}\text{ x 2}\pi r \\ where\text{ }\theta\text{ = 45}^0 \\ Radius\text{ = 9 inches} \\ \end{gathered}[/tex][tex]\begin{gathered} Arc\text{ length =}\frac{45^0}{360^0}\text{ x 2 x }\pi\text{ x 9} \\ =\frac{1}{8}\text{ x 2 x }\pi\text{ x 9} \\ =\text{ }\frac{18\pi}{8} \\ =\text{ }\frac{9\pi}{4} \\ =\text{ 7.068583471} \\ \approx\text{ 7.07 inches \lparen correct to 2 decimal places\rparen} \end{gathered}[/tex]CONCLUSION:
The length of the Arc = 7.07 inches ( correct to 2 decimal places )
I need help please!!!! I need the answer like right now please!! Thank you!!!
Please give me the correct answer.True or false.If a=b,then a+c=b+c.
The statement is true since it is the so-called Addition Property of Equality, which says that, if two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal.
Find how much money needs to be deposited now into an account to obtain $7,400 (Future Value)
in 10 years if the interest rate is 7% per year compounded monthly (12 times per year).
The final amount is $
Round your answer to 2 decimal places
Given a certain rate of return, present value (PV) is the current value of a future sum of money or stream of cash flows.
$ 3,682.21 is the present value.
How to find the present value?A future sum of money or stream of cash flows' present value (PV), assuming a given rate of return, is their current value.
Future value is converted to present value by using either a discount rate or the interest rate that would be earned if an investment were made.
Present Value = FV/(1+r/n)^nt
Solution:
Present Value = FV/(1+r/n)^nt
Present Value = 7400/(1+7/12)^10*12
Present Value = 7400/(19/12)^120
Present Value = 7400/(1.58)^120
Present Value = 7400/2^120
Present Value = $ 3,682.21
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how many ways can Aileen choose 2 pizza toppings from a menu of 19 toppings if each topping can be chosen once ?
Answer:
[tex]171\text{ ways}[/tex]Expalnation:
From what we have here, there are 19 toppings to choose from
To choose the first topping, there are 19 choices to select from
For the second topping selected, since repetition is not allowed, there would be 17 toppings to choose from
Thus, the total number of ways will be according to the combination rule as follows:
[tex]\begin{gathered} ^nC_r\text{ = }\frac{n!}{(n-r)!r!} \\ ^{19}C_2\text{ = }\frac{19!}{(19-2)!2!}\text{ = 171 ways} \end{gathered}[/tex]A biker is making a turn around the corner. The biker's speed remained constant at 12 miles per hour during the entire turn. Which of the following statements describes the forces on the biker?
The forces were balanced to keep the biker with a constant speed.
The forces were unbalanced as the biker made the turn.
The forces were balanced due to the biker's inertia.
The forces were unbalanced due to the action-reaction pair required to turn.
The forces were balanced due to the biker's inertia. Option C.
Objects that move in circles or along circular orbits experience a centripetal force. That is there is a physical force pushing or pulling an object toward the center of the circle. The centripetal force that causes the car to spin in a circle is generated by the friction between the tires and the road surface. A minimum coefficient of friction is required. Otherwise, the car will travel a curve with a larger radius and leave the lane.
As the motorcycle climbs the loop friction forces act along the direction of travel to prevent gravity from slowing it down. As the motorcycle descends the loop friction forces act against the direction of motion preventing acceleration due to gravity. Whenever the velocity increases at the same rate, we are moving with constant acceleration. Centripetal force supports the circular motion. One idea is that if the road is smooth the car can't make a circle.
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Answer: The forces were balanced due to the biker's inertia.
Step-by-step explanation:
option c
3/9 divided by 10/50
To be able to divide the two fractions as given,
I need help with this practice Can you solve, please explain step-by-step, *as I am new to this branch/topic of math*
Explanation
This is Algeba, an aspect of Math
We are told to find th correct optionthat satisfies the condition of a and b
Given that
a =5 and b =8
To go about this, we will simply substitute a = 5 and b=8 into each of the equation and cross-check the value with 104
Let us check for the first option
[tex]\begin{gathered} 8+a+8+b \\ 8+5+8+8=29 \\ since\text{ 29 is not equal to 104, then this is a wrong answer} \end{gathered}[/tex]Option B
[tex]\begin{gathered} 8+a+8b \\ 8+5+8(8)=8+5+64=77 \\ since\text{ 77 is not equal to 104, then this is wrong also} \end{gathered}[/tex]Option C
[tex]\begin{gathered} 8a+8+b=8(5)+8+8=40+16=56 \\ since\text{ 56 is not equal to 104, then this is also wrong} \end{gathered}[/tex]Option D
[tex]\begin{gathered} 8a+8b=8(5)+8(8)=40+64=104 \\ \\ 104\text{ is EQUAL to 104} \\ This\text{ is correct} \end{gathered}[/tex]Therefore, the anser is
how can I construct a tally table to represent the data?
Answer:
a)
To construct a tally table, we will have to present the table ranging from 150 to 156
b)
The probability of choosing a student not more than 153 in height means
[tex]\begin{gathered} Pr(h\leq153) \\ Pr(h\leq153)=\frac{n(h\leq153)}{n(S)} \\ (h\leq153)=1+5+10+16=32 \\ n(S)=50 \\ Pr(h\leq153)=\frac{n(h\leq153)}{n(S)}=\frac{32}{50}=\frac{16}{25} \end{gathered}[/tex]Hence,
The probability of picking not more than 153cm in height is = 16/25
b ii)
To figure out the probability greater than 153cm in height
[tex]\begin{gathered} Pr(h>153) \\ Pr(h>153)=\frac{n(h>153)}{n(S)} \\ n(h>153)=10+6+2=18 \\ n(S)=50 \\ Pr(h>153)=\frac{n(h>153)}{n(S)}=\frac{18}{50}=\frac{9}{25} \end{gathered}[/tex]Hence,
The probability of height greater than 153cm = 9/25
The following table shows the points scored each game by Pat during the basketball season. Complete the following questions:1. What is the probability Pat scores between 10 and 15 points in a game? Round answer to two decimal places.2. What is the probability Pat scores 16 or more points? Round answer to three decimal places.
ANSWER
[tex]\begin{gathered} (1)0.162 \\ (2)0.811 \end{gathered}[/tex]EXPLANATION
From the given table;
1. The probability that Pat scores between 10 and 15 points in a game;
The frequency for (10 - 15) is 6
Summation of frequency is;
[tex]1+6+5+17+8=37[/tex]Hence, the probability that Pat scores between 10 and 15 points in a game;
[tex]\begin{gathered} P(10\leq x\leq15)=\frac{6}{37} \\ =0.16216 \\ \cong0.162 \end{gathered}[/tex]2. The probability Pat scores 16 or more points is calculated by adding all the frequency from 16 points and above.
Hence;
[tex]5+17+8=30[/tex]Therefore the P(16 and above);
[tex]\begin{gathered} P(x\ge16)=\frac{30}{37} \\ =0.8108 \\ \cong0.811 \end{gathered}[/tex]Use the two-way frequency table to calculate the probability that the person is a democrat, given theact that the person supports the issue, P(democrat | supports the issue).P(democrat | supports the issue) =(Type an integer or decimal rounded to the nearest hundredth as needed.)
In order to calculate the probability of P(democrat | supports the issue), we can use the following formula for conditional probability:
[tex]\begin{gathered} P(A|B)=\frac{P(A\cap B)}{P(B)} \\ P(democrat|supportstheissue)=\frac{P(democrat\cap supportstheissue)}{P(supportstheissue)} \end{gathered}[/tex]In the right side of the equation, instead of using the probability, we can use the value in the frequency table.
So we have:
[tex]P(democrat|supportstheissue)=\frac{24}{58}=\frac{12}{29}=0.41[/tex]I need help finding the vertex and axis of symmetry
To find the vertex coordinates from the parabola, you can analyze the graph. The x (vertex) coordinate is just over the "x" axis, so the value is xvertex = 2.
The y (vertex) coordinate is y= 0 because it is the value that the parabola takes on that axis.
The axis of symmetry is the value in the "x" axis where the parabola is divided in half. So in this case is x = 2.
So the anser is x(vertex) = 2, y (vertex)=0 , and the axis of symmetry is x= 2.
13. There is an 80 gram mixture of material X, Y, and Z. The ratio X :Y:Z is 4/7 / 5 . If material Z is removed, what is the new weight, in gram, of the mixture?A. 11B.64C. 25D.45
The ratio given in the problem implies that for every 4 gr of X in the mixture, there are 7 gr of Y and 5 gr of Z. Notice that:
[tex]\begin{gathered} 4+7+5=16 \\ \frac{80}{16}=5 \end{gathered}[/tex]Then, we need to multiply all the previous quantities by 5. Then, in the 80gr mixture, there are 20gr of X, 35gr of Y, and 25gr of Z.
If we remove Z from the mixture, we will end up with a total mass of:
[tex]80-25=55[/tex]55 gr is the answer to the question, despite not being among the options
Prove that the options given are not possible:
Notice that options A and C imply that most of the mixture consists of Z substance, which is not possible according to the relation.
The only possibility would be C, in that case:
[tex]\begin{gathered} 4+7=11 \\ \frac{64}{11}=5.8181\ldots \\ \Rightarrow Z\approx29.0909\ldots \\ 64+29.0909\approx93.0909 \end{gathered}[/tex]Which is not equal to 100gr
select all input values for which f(x)=2.choose all answers that apply:A.) x= -7B.) x=0C.) x=4D.) None of the above
The expression f(x) = 2 refers to all the x-value that make y = 2.
According to the given graph, the value is x = -7 because that's where y = 2.
Hence, the answer is A.A soup company is looking at two designs for a new can. Can a have a diameter of 8 centimeters and a height of 15 centimeters. Can B has diameter of 10 centimeters and a height of 12 cm. How much greater of the volume of can B then can A? Use 3.14 for π and give the difference to The nearest cubic centimeter. To the nearest cubic centimeter, volume to Cube B is ______ centimeters.
Given:
The diameter of can A is, d(A) = 8 cm.
The height of can A is, h(A) = 15 cm.
The diameter of can B is, d(B) = 10 cm.
The height of can B is, h(B) = 12 cm.
The objective is to find how much greater is volume of can B than can A.
Explanation:
The general formula for volume of a can is,
[tex]V=\pi r^2h[/tex]To find volume of A:
The volume of can A can be calculated as,
[tex]V(A)=\pi(\frac{d_A}{2})^2\times h_A\text{ . . .. . .. (1)}[/tex]On plugging the given values in equation (1),
[tex]\begin{gathered} V(A)=3.14\times(\frac{8}{2})^2\times15 \\ =753.6\operatorname{cm}^3 \end{gathered}[/tex]To find volume of B:
The volume of can B can be calculated as,
[tex]V(B)=\pi(\frac{d_B}{2})^2h_B\text{ . . . . .(2)}[/tex]On plugging the given values in equation (2),
[tex]\begin{gathered} V(B)=3.14\times(\frac{10}{2})^2\times12 \\ =942\operatorname{cm}^3 \end{gathered}[/tex]To find difference:
The difference between volume of can A and can B will be,
[tex]\begin{gathered} V(B)-V(A)=942-753.6 \\ =188.4\operatorname{cm}^3 \end{gathered}[/tex]Hence, the volume of can B is greater than can A by 188.4 cm³.
compare f(0) and g(0)g(x)=|2x-8|-11f(0) is =, <, or > than g(0)
Let's begin by listing out the given information:
For the graph of f(x), we will pick out two coordinates that lie along the straight line. We have:
[tex]undefined[/tex]Find the value of xOptions are 110, 80, 35, 40
The sum of all angles in a triangle is 180º. Therefore:
[tex]\begin{gathered} 180=\text{ 30 + \lparen3x-10\rparen + x} \\ 180=\text{ 30 +3x -10 + x} \\ 180\text{ = 20 + 4x} \\ 180\text{ - 20 = 4x} \\ 160=\text{ 4x} \\ \\ \frac{160}{4}=\text{ x} \\ \\ 40=\text{ x} \end{gathered}[/tex]X will be 40º.
Find the number of solutions of the equation 6x2 + 6x + 3 = 0 by using the discriminant
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the standard form of a quadratic equation
[tex]ax^2+bx+c=0[/tex]STEP 2: Write the formula for getting a discriminant
[tex]D=b^2-4ac[/tex]STEP 3: Write the given quadratic equation
[tex]\begin{gathered} 6x^2+6x+3=0 \\ a=6,b=6,c=3 \end{gathered}[/tex]STEP 4: Substitute the values to get the discriminant
[tex]\begin{gathered} D=6^2-4(6)(3) \\ D=36-72=-36 \\ D=-36 \end{gathered}[/tex]STEP 5: Explain the conditions for using the discriminant
If the discriminant is greater than zero, there are two solutions.
If the discriminant is equal to zero, there is one real solution
If the discriminant is less than zero, there are no real solutions
Hence, using the conditions above,
There are no real solutions since the discrimian
PLEASE HELP IM SICK AND I DONT UNDERSTAND.DUE IN 30 MINS!!!!!!
The value of x is -12 and the pair of interior angles are: 130 and 50 degrees.
Given, a transversal is passed by the parallel lines.
Hence consecutive interior angles are formed.
Each pair of internal angles on the same side of a transversal are supplementary, or they add up to 180°, if the transversal meets two parallel lines.
therefore, x+142 + x + 62 = 180°
arrange the variables one side
2x + 142 + 62 = 180
add the constants.
2x + 204 = 180
2x = 180-204
2x = -24
x = -12
interior angle 1 = x+142
= -12+142
= 130°
interior angle 2 = x+62
= -12+62
= 50°
Hence the value of x is -12.
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(x^4)+(5x^2)+4=1 i need help on how to do this
Name the set of 4 consecutive odd integers starting with -3 ( put the set in braces [ ] and put commas between the elements of the set. )
Solution
For this case we need to find 4 consecutive odd integers so we can do this:
-3, -3+2, -3+2+2, -3+2+2+2
Solving we got:
[-3,-1, 1, 3]
please put answers for sin, cos, tan, cot, sec, and csc
If we measure the angle in the clockwise direction:
Therefore, this point is:
[tex](-1,0)[/tex]Since the cosine and sine functions are given by:
[tex]\begin{gathered} \sin (\theta)=\frac{opposite}{_{\text{ }}hypotenuse} \\ \cos (\theta)=\frac{adjacent}{_{\text{ }}hypotenuse} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \sin (-\pi)=\frac{0}{1}=0 \\ \cos (-\pi)=\frac{1}{-1}=-1 \end{gathered}[/tex]Since:
[tex]\begin{gathered} \cot (\theta)=\frac{adjacent}{_{\text{ }}opposite}\to\cot (-\pi)=-\frac{1}{0}=_{\text{ }}undefined \\ \csc (\theta)=\frac{hypotenuse}{_{\text{ }}opposite}\to\csc (-\pi)=\frac{1}{0}=_{\text{ }}undefined \end{gathered}[/tex]Therefore, we can conclude that cotangent and cosecant are undefined for - π
[tex]\begin{gathered} \tan (\theta)=\frac{opposite}{_{\text{ }}adjacent}=\frac{0}{-1}=0 \\ \sec (\theta)=\frac{hypotenuse}{_{\text{ }}adjacent}=\frac{1}{-1}=-1 \end{gathered}[/tex]
