The graph of the function y=x^2+2 is shown. Which equation will shift the graph of the function to the right 2 units?
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"you want to buy a new sports car from roy's cars for $51,800. the contract is in the form of a 48-month annuity due at a 9.2 percent apr. what will your monthly payment be"
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Answer: $1,284.13
Step-by-step explanation:
a piece of baseboard is 2/3 yard long. Angela cuts the board into pieces that are 1/6 yard long. How many pieces are there
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[tex]\bf \cfrac{\quad \frac{2}{3}\quad }{\frac{1}{6}}\implies \cfrac{2}{3}\cdot \cfrac{6}{1}\implies \cfrac{2}{1}\cdot \cfrac{2}{1}\implies 4[/tex]
Let , 4 ,− 7 be a point on the terminal side of θ . find the exact values of cos θ , csc θ , and tan θ .
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First thing first. We need to see if we are working with a unit circle and find the radius.
How to tell if we are working with a unit circle?
We know [tex]x^2 + y^2 = r^2[/tex] is a circle.
We know that to find the radius we can use the following formula:
[tex]r^2 = \sqrt{x^2 + y^2}[/tex]
If [tex]r^2 = \sqrt{x^2 + y^2} = 1[/tex] we are working with a unit circle.
Lets see if it = 1.
[tex]r^2 = \sqrt{4^2 + -7^2}[/tex]
[tex]r^2 = \sqrt{16 + 49}[/tex]
[tex]r^2 = \sqrt{65}[/tex]
Square both sides now
[tex]\sqrt{r^2} = \sqrt{\sqrt{65}}[/tex]
[tex]r = \pm 65^{\frac{1}{4}}}[/tex]
Since we squared, we have a + and a - but we disregard the - because we do not have - radii
[tex]r = 65^{\frac{1}{4}}}[/tex]
We can also say
[tex]r = \sqrt[4]{65}[/tex]
Ok, since r does not equal 1, we are not working with a unit circle but we have found r, which is our radius.
Now that we know the value of r, which is [tex]r = 65^{\frac{1}{4}}}[/tex], we need to look at the identities of cos, csc and tan.
The identities:
[tex]cos \theta = \frac{x}{r}[/tex]
[tex]csc \theta = \frac{1}{y}[/tex]
[tex]tan \theta = \frac{y}{x}[/tex]
Now that we know their identities and know the radius of our circle, we can find the exact values of cos, csc and tan.
[tex]cos \theta = \frac{x}{r} = \frac{4}{65^{\frac{1}{4}}}[/tex]
[tex]csc \theta = \frac{1}{y} = \frac{1}{-7}[/tex]
[tex]tan \theta = \frac{y}{x} = \frac{-7}{4}[/tex]
The exact values for cos, csc and tan given the point (4,-7) are:
[tex]cos \theta = \frac{4}{65^{\frac{1}{4}}}[/tex]
[tex]csc \theta = \frac{1}{-7}[/tex]
[tex]tan \theta = \frac{-7}{4}[/tex]
The exact values are [tex]\cos \theta = \frac{4\sqrt{65}}{65}[/tex], [tex]\csc \theta = \frac{\sqrt{65}}{4}[/tex] and [tex]\tan \theta = -\frac{7}{4}[/tex], respectively.
Let be a Point of the form [tex](x,y)[/tex] that is the Terminal Side of angle [tex]\theta[/tex], in sexagesimal degrees. By Trigonometry, we know that the Cosine, Cosecant and Tangent of the Angle are, respectively:
[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex] (1)
[tex]\csc \theta = \frac{\sqrt{x^{2}+y^{2}}}{y}[/tex] (2)
[tex]\tan \theta = \frac{y}{x}[/tex] (3)
If we know that [tex]x = 4[/tex] and [tex]y = -7[/tex], then the exact value of all the trigonometric relations are:
[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex]
[tex]\cos \theta = \frac{4}{\sqrt{4^{2}+(-7)^{2}}}[/tex]
[tex]\cos \theta = \frac{4\sqrt{65}}{65}[/tex]
[tex]\csc \theta = \frac{\sqrt{x^{2}+y^{2}}}{y}[/tex]
[tex]\csc\theta = \frac{\sqrt{4^{2}+(-7)^{2}}}{4}[/tex]
[tex]\csc \theta = \frac{\sqrt{65}}{4}[/tex]
[tex]\tan \theta = \frac{y}{x}[/tex]
[tex]\tan \theta = -\frac{7}{4}[/tex]
The exact values are [tex]\cos \theta = \frac{4\sqrt{65}}{65}[/tex], [tex]\csc \theta = \frac{\sqrt{65}}{4}[/tex] and [tex]\tan \theta = -\frac{7}{4}[/tex], respectively.
Please see the related question for further details: https://brainly.com/question/15225546
As viewed from above, a swimming pool has the shape of the ellipse x24900+y22500=1, where x and y are measured in feet. the cross sections perpendicular to the x-axis are squares. find the total volume of the pool. v = cubic feet
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a=sqrt(4900)=70
b=sqrt2500=50
The squares are parallel to the y-axis, thus their sides extend in the y-axis direction, hence the length of the sides are:
y=+/-50sqrt(1-x^2/4900))
The area of the square
=y^2=[2500-2500(x^2/4900)
Thus, the volume will be sum along the x-axis from one of the ends of the ellipse to the other. by definition, the limits are (-a to a)=(-70 to 70)
But since the ellipse is symmetrical we can go from (0 to 70) and double the integral.
thus
V=2*int(0 to 70)[2500-2500(x^2/4900)]dx
=int(0 to 70)[5000-(50/49)x^2]dx
=[5000x-50/147x^3] (0 to 70)
=233,333 1/3 ft^3
The amount of money that a student at harvard university carries on his/her person is normally distributed with a mean of $25 and a standard deviation of $15. what is the probability that a randomly selected sample of 25 harvard university students will have an average amount of less than $22 on his/her person?
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Standard deviation, s = $15
Sample size, n = 25 students
X <$22
Now,
Z = [(X - m)*Sqrt (n)]/s = [(22-25)*Sqrt(25)]/15 = -1
From Z tables,
P(X) = P(Z = -1) = 0.1587 = 15.87%
Therefore, probability that the selected sample has an average of less than $22 is 15.87%.
How do you evaluate this equation: a number decreased by the difference of m and 7? Please help and quick!!
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A number decreased by the difference of m and 7 can be translated into mathematical expression as
[tex]n-\left(m-7\right)[/tex]
Which graph best represents the equation -4x + 5y = 10?
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Do you have a photo to show the separate graphs?
Answer: these are the graphs and i need the answer
Step-by-step explanation:
is this correct if not help me
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You have properly counted squares and circles.
A large construction company wants to review the ages of its sales representatives. A sampling of the ages of 25 sales reps are given: 50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45 The following histogram is a representation of the data. Calculate the median ages
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22, 24, 28, 28, 30, 31, 31, 32, 32, 35, 36, 37, 38, 41, 42, 42, 44, 44, 45, 46, 46, 47, 47, 49, 50
Once you put them into order, you count towards the middle. You have 25 data points, so the middle, which will be your median number, will be 13 points in.
The median is 38
The median age of the sales representatives is 37.5 years.
Explanation:To find the median ages of the sales representatives, we first need to order the ages in ascending order:
Since there are 25 data values, the middle value will be the median age. To find the middle value, we divide the number of data values by 2, which gives us 12.5. Since the median is the average of the two middle values, we can take the average of the 12th and 13th values in our ordered list:
Median age = (37 + 38) / 2 = 37.5 years
When subtracted, what is the simplified form of (5 − 3i) − (4 + 6i)? Write the answer in standard form, a + bi, where a and b are real numbers.
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5 - 3i - 4 - 6i Did you notice how the second set worked. That - sign affected both terms inside the brackets. Now collect your like terms.
5 - 4 - 3i - 6i The - 3i and - 6i act like money. You are three dollars in the hold and you spend another 6. Where does that put you ?
1 - 9i You are now 9 dollars in the whole.
The sides of a rectangle are in the ratio of 4:5. If the width is 28 in., find the length, the perimeter, and the area of this rectangle.
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Length: 35 in
Perimeter: 126 in
Area: 980 inches squared.
Suppose that 5 green balls and 12 purple balls are placed in an urn. two balls are then drawn in succession. what is the probability that the second ball drawn is a purple ball if the first ball is replaced before the second is drawn?
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Total number of balls = 5 + 12 = 17
Total number of purple balls = 12
P(second one is purple) = 12/17
Answer: 12/17
Uisng the concept of probability, the probability that the second ball drawn is purple is 12/17
Given the Parameters :
Number of green balls = 5 Number of purple balls = 12Total number of balls = 12 + 5 = 17
Recall :
Probability = required outcome / Total possible outcomesSince selection is made with replacement :
P(purple) = number of purple balls / total number of balls
P(purple) = 12/17Therefore, the probability of drawing a purple ball is 12/17
Learn more : https://brainly.com/question/18796573
A rancher has 300 feet of fencing to enclose a pasture bordered on one side by a river. the river side of the pasture needs no fence. find the dimensions of the pasture that will produce a pasture with a maximum area.
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A cleaner recommends mixing 1 1/2 cup of cleaner for every 12 cups of water. What is the ratio of cleaner to water in simplest form?
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cleaner:water
1 1/2:12
simplifying the above we get:
3/2:12
multiplying both sides by 2 we get:
2×3/2:12×2
3:24
hence the answer is 3:24
four friends share 3 fruits bars equally how much does each friend get
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each friend gets 0.75 of a bar
with an 18% discount, George was able to save 13.23 what was the original price
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1% = $13.25 ÷ 18 = $0.7361
100% = $0.7361 x 100 = $73.61
Answer: $73.61
One serving of Mike’s crackers has 150 calories and a mass of 30 grams. How many calories are in 6 grams of the crackers?
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The amount of calories that are in 6 grams of crackers is 30 grams.
What is the amount of calories in the crackers?Division is the mathematical operation that is used to determine the quotient of a number. It is the process of grouping a number into equal parts using another number.
Calories in 6 grams = (150 / 30) x 6 = 30 grams
To learn more about division, please check: https://brainly.com/question/13281206
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Final answer:
To find the calories in 6 grams of Mike's crackers, divide the total calories by the total mass of one serving to get the unit rate (5 calories/gram) and then multiply by the mass in question (6 grams) to obtain 30 calories.
Explanation:
The question asks how many calories are in 6 grams of Mike's crackers, given that one serving of 30 grams has 150 calories. To find the calories in 6 grams of the crackers, we can use unit rate and proportions.
Step-by-Step Calculation
First, determine the calories per gram of the crackers by dividing the total calories by the total mass (in grams) of one serving. This gives us the unit rate: 150 calories / 30 grams = 5 calories per gram.
Next, since we're asked about the calories in 6 grams, we multiply the calories per gram (unit rate) by the mass: 5 calories/gram × 6 grams = 30 calories.
Therefore, there are 30 calories in 6 grams of Mike's crackers. This calculation illustrates the utility of understanding proportions and unit rates in everyday applications such as determining caloric intake from portions of food.
hey can you please help me posted picture of question
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1. You have the following expression:
(11-7i)-(16-11i)
2. If you want to substract both terms, you need to substract the real numbers and the complex numbers. Then, you obtain:
11-7i-16+11i
(11-16)+(-7+11)
3. Then, you obtain the following result:
-5+4i
4. Therefore, as you can see, the correct answer is the second option (option B), which is:
B. -5+4i
Solution is shown below:
To add or subtract two complex numbers, the real part is added or subtracted from real part and the complex part is added to or subtracted from complex part as shown below:
(11 - 7i) - (16 - 11i)
= 11 - 7i - 16 + 11i
= -5 + 4i
So, the answer to this question is option B
find the length of the side f .
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[tex]10 {}^{2} + 15 {}^{2} = 18 {}^{2} \\ 100 + 225 = 325 \\ \sqrt{325} = 18 [/tex]
Using Pythagorean Theorem, you have the hypotenuse or side "c" (18) which is longest side. You also have side "b" (15).
Since the equation is "a^2 + b^2 = c^2”, fill in for "b" and "c" giving "a^2 + 15^2 = 18^2"
Solve for "a". Square each known value, leaving "a^2 + 225 = 324". Subtract 225 from each side, leaving "a^2 = 99" then use the square root on each side. Thus getting "a = 9.94987..., which rounded up is 9.95.
I hope this helps!
in the plane figure shown below. if the degree measures of the angle are as shown, then x+y=
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the sum of the internal angles in the figure shown is 360 degrees
so
360°=100°+60+70°+y+80°+x
360°=(x+y)+310°
(x+y)=360°-310°-----> 50°
the answer is
x+y is 50°
Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 8.4 seconds. suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is less than 8.4 seconds. what would you use for the alternative hypothesis?
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what is the area of a square with a radius of 9 cm
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If you mean the area of a circle with a 9cm radius, then it would be 254.34 cm squared.
Under what circumstances is a t statistic used instead of a z score for a hypothesis test
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a game has a deck of cards with 10 red cards, 4 blue cards, and 2 yellow cards. you randomly choose two cards(choose one and choose the second one without replacement) find the probability of choosing a blue card and a yellow card
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[tex] \displaystyle
|\Omega|=\binom{16}{2}=\dfrac{16!}{2!14!}=\dfrac{15\cdot16}{2}=120\\
|A|=4\cdot2=8\\\\
P(A)=\dfrac{8}{120}=\dfrac{1}{15}\approx7\% [/tex]
What is the equation for the graph shown below?
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the common view of the required equation is y=(x-a)(x-b), where 'a' and 'b' are the interception points (the curve and Ox).
using the coordinates of interception points it is possible to make up the required equation: x=3 and x=5.
y=(x-3)(x-5).
If to check the equation using the coordinates of the vertex (4;-1):
-1=(4-3)(4-5) ⇔ -1=-1, it means, that the equation made up is correct.
answer: y=(x-3)(x-5) or y=x²-8x+15.
There are 12 people having lunch.Each person wants 1/3 of a sub sandwich.How many whole sub sandwiches are needed ?use models to show answer.
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A listing of all possible outcomes of an experiment and their corresponding probability of occurrence is called
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The listing of all possible outcomes for an experiment is known as a probability distribution.
The following information is related to the probability distribution is:
It is the table or an equation that is connected with each and every result of the statistical experiment along with the probability of occurrence.Also, it is the list of all possible experiment results.Therefore we can conclude that the listing of all possible outcomes for an experiment is known as a probability distribution.
Learn more: brainly.com/question/22174871
What is the area of this figure?
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6 * 5 = 30
The area of the second rectangle is calculated by multiplying its length and width:
12 * 4 = 48
Now, we can add the areas to find the total area of the figure:
30 + 48 = 78
The figure's area is 78 cm².
A soccer ball is kicked from the ground in an arc defined by the function, h(x) = -2x 2 + 8x. At what point does the ball hit the ground?
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anyhow, it hits the ground at two points, when it began, and when it came back down, and that happens when y = 0.
[tex]\bf h(x)=-2x^2+8x\implies \stackrel{h(x)}{0}=-2x^2+8x\implies 0=-2x(x-4)\\\\ -------------------------------\\\\ 0=-2x\implies 0=x\qquad \impliedby \textit{when it began}\\\\ -------------------------------\\\\ 0=x-4\implies \boxed{4=x}\qquad \impliedby \textit{when it came back down}[/tex]
Answer:
4 seconds
Step-by-step explanation:
h(t) = -3t^2 + 12t
0 = -3t^2 + 12t
0 = -3t(t - 4)
0 = t - 4
t = 4
Therefore, it takes 4 seconds for the rocket to hit the ground.
hope it helps :)
mark brainliest!
I have two bags. bag 1 contains 1010 blue marbles, while bag 2 contains 1515 blue marbles. i pick one of the bags at random, and throw 66 red marbles in it. then i shake the bag and choose 55 marbles (without replacement) at random from the bag. if there are exactly 22 red marbles among the 55 chosen marbles, what is the probability that i have chosen bag 1
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55-22 = 33 blue marbles
bag1+bag2= 2525
bag1=.4
33/55=.6 blue marbles
bag 2=.6
so it is 40% that U choose bag 1