Parking lots A and B charge a set fee. A charges 36.50 for 5 hours. B charges 38.00 for 5 hours. Lot A charges 49.50 for 7 hours and lot B charges 50.00 for 7 hours. How many hours are needed to park where it would cost the same?
Answer:
if you park for 12 hours in both parking lots A and B, it will cost the same amount, which is $64.50.
Step-by-step explanation:
Let's assume that the cost of parking for x hours in both lots is the same, then we can set up the following equations:
For 5 hours of parking:
36.50 = 38.00
This is not true, so we know that the cost for parking in both lots will not be the same for 5 hours.
For 7 hours of parking:
49.50 = 50.00
This is also not true, so we know that the cost for parking in both lots will not be the same for 7 hours either.
Let's try setting up the equation for x hours of parking:
Fee for parking in Lot A = Fee for parking in Lot B
36.50 + (x-5)*7 = 38.00 + (x-5)*7
Simplifying the equation, we get:
36.50 + 7x - 35 = 38.00 + 7x - 35
Solving for x, we get:
x = 12
Therefore, if you park for 12 hours in both parking lots A and B, it will cost the same amount, which is $64.50.
Which of the following points is in the solution set of y < x^2 - 2x - 8?
The points that is in the solution set of y < x² - 2x - 8 is option A: (-2, -1)
What is the solution about?When you Check the inequality by (-2,-1) then Put x=-2 and y=-1 in the given inequality.
1 < (-2)² - 2(-2) - 8
-1 < 4 + 4 - 8
-1 < 0
Hence:
(-2,-1) can be in the solution
( 0,-2) Cannot
(4,0) will not.
Therefore, The points that is in the solution set of y < x² - 2x - 8 is option A: (-2, -1)
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See full question below
Which of the following points is in the solution set of y < x2 - 2x - 8?
(-2, -1)(0, -2)(4, 0)
A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 5 ft by 14.5 ft by 6.5 ft. If the container is entirely full and, on average, its contents weigh 0.3 pounds per cubic foot, find the total weight of the contents. Round your answer to the nearest pound if necessary.
The total weight of the contents is 141.33 pounds.
What is a rectangular prism?
A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.
Here, we have
Given: A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 5 ft by 14.5 ft by 6.5 ft. The container is entirely full and, on average, its contents weigh 0.3 pounds per cubic foot.
The volume of the container is calculated as:
5 ft× 14.5 ft× 6.5 ft= 471.125 ft³
Then, the total weight of the contents is calculated as:
471.125 ft³× 0.3 pounds per cubic foot= 141.3375 pounds≅ 141.33 pounds
Hence, the total weight of the contents is 141.33 pounds.
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. To determine how funny the jokes were, the researchers asked a group of 86 undergraduates to rate the jokes on a scale from 1 (very unfunny) to 21 (very funny). Participants rated a “lawyer joke” as one of the funniest jokes, with a rating of 14.48 ± 4.38 (M ± SD).
Assuming that these data are normally distributed,
1. What was the rating that marks the cutoff for the top 10% of participant ratings for this joke?
If the "Lawyer's-Joke" is rates as the funniest, then the rating which is the top 10% of participant rating for this joke is 20 marks.
A "Normal-Distribution" is defined as a probability distribution that is symmetric, bell-shaped, and characterized by its mean and standard deviation.
First, we standardize the rating of 14.48 using the formula:
⇒ z = (x - μ) / σ;
where x is = rating of 14.48, μ is = mean rating, and σ is = standard deviation,
⇒ z = (14.48 - 14.48) / 4.38,
⇒ z = 0,
Next, we take the "z-score" that corresponds to the top 10% of the standard normal distribution. We know that the "z-score" is approximately 1.28,
Substituting the value in formula,
We get,
⇒ z = (x - μ) / σ ⇒ 1.28 = (x - 14.48)/4.38,
⇒ x - 14.48 = 1.28 × 4.38,
⇒ x = 20.97 ≈ 20 marks.
Therefore, the rating that marks the cutoff for the top 10% of participant ratings for this joke is approximately 20 on the scale of 1 to 21.
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Point P is on the terminal side of angle theta.
Find cot of theta.
Point P is located at (0, 5)
Check the picture below, so the angle looks more or less like so.
now, let's recall that the value pair in a terminal point is the adjacent and opposite sides
[tex]\cot(\theta )=\cfrac{\stackrel{adjacent}{0}}{\underset{opposite}{5}}\implies \cot(\theta )=0[/tex]
Quiz Active
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Which dimensions can create more than one triangle?
three angles measuring 25°, 65°, and 90°
three angles measuring 50°, 50°, and 50°
three sides measuring 5 in., 12 in., and 13 in.
three sides measuring 4 ft, 8 ft, and 10 ft
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The dimensions that can create more than one triangle are given as follows:
three angles measuring 25°, 65°, and 90°.
What is the law of sines?Suppose we have a triangle in which:
Side with a length of a is opposite to angle A.Side with a length of b is opposite to angle B.Side with a length of c is opposite to angle C.The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
The sum of the measures of the internal angles of a triangle is of:
180º.
Meaning that the first option is correct and the second is not.
Considering the law of sines, an infinite number of triangles can be formed, as long as:
sin(25º)/a = sin(65º)/b = sin(90º)/c.
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248 meters per second = miles per hour
Answer:
554.76 miles per hour
Step-by-step explanation:
[tex]\frac{248 meters}{1 second}[/tex] x [tex]\frac{3600 seconds}{1 hour}[/tex] x [tex]\frac{1 mile}{1609.34 meters}[/tex]
= 554.76 miles per hour
[tex]\sf 554.76(mi/h).[/tex]
Step-by-step explanation:1. Write the initial expression.[tex]\sf \dfrac{248(m)}{s}[/tex]
2. Using conversion factors, convert from meters to miles.a) First, convert the meters to kilometers.
[tex]\sf 248(m)*\dfrac{1(km)}{1000(m)} =0.248(km)[/tex]
Here, the meters cancel, since one is on the numerator and the other one is expressed as a denominator, and we simpyl multiply the value by the fraction, resulting in a number that would be a value for kilometers.
b) Convert from kilometers to miles.
[tex]\sf 0.248(km)*\dfrac{1(mi)}{1.60934(km)} =0.1541(mi)[/tex]
3. Convert the seconds into hours.[tex]\sf 1(seconds)*\dfrac{1(hour)}{3600(seconds)} =\frac{1}{3600}(h)[/tex]
4. Rewrite the initial expression using the calculated converted values.[tex]\sf \dfrac{0.1541(mi)}{\dfrac{1}{3600} (h)} =554.76(mi/h)[/tex]
Question 1(Multiple Choice Worth 2 points)
(Slope-Intercept Form MC)
The amount of laps remaining, y, in a swimmer's race after x minutes can be represented by the graph shown.
coordinate grid with the x axis labeled time in minutes and the y axis labeled number of laps remaining with a line from 0 comma 24 and 6 comma 0
Determine the slope of the line and explain its meaning in terms of the real-world scenario.
The slope of the line is 6, which means that the swimmer will finish the race after 6 minutes.
The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.
The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.
The slope of the line is negative one fourth, which means that the swimmer completes a lap in one fourth of a minute.
Question 2(Multiple Choice Worth 2 points)
(Systems of Linear Equations MC)
Two siblings, sibling A and sibling B, are saving money for their summer vacation. The amount of money that sibling A has in their savings account, y, can be represented by the equation y = 10x + 25, where x represents the number of weeks. Sibling B's savings can be represented by the equation y = 5x + 50.
Based on the graph of this system of linear equations, after how many weeks will their savings accounts have the same amount of money?
2.5 weeks
5 weeks
15 weeks
75 weeks
Question 3(Multiple Choice Worth 2 points)
(Identifying Transformations LC)
Polygon ABCD is rotated to get polygon A′B′C′D′.
Graph of polygon ABCD in quadrant 2 with point A at negative 7 comma 5, point B at negative 2 comma 8, point C at negative 2 comma 4, and point D at negative 4 comma 3 and polygon A prime B prime C prime D prime in quadrant 1 with point A prime at 5 comma 7, point B prime at 8 comma 2, point C prime at 4 comma 2, and point D prime at 3 comma 4
Determine the direction and angle of rotation.
270° clockwise rotation
270° counterclockwise rotation
90° counterclockwise rotation
180° clockwise rotation
Question 4(Multiple Choice Worth 2 points)
(Scatter Plots MC)
Data was collected on the price per cupcake on orders of different amounts from a bakery. The scatter plot shows the data that was gathered.
scatter plot titled cupcake pricing with the x axis labeled number of cupcakes and the y axis labeled cost per cupcake in dollars with points at 1 comma 6, 2 comma 5, 2 comma 5.5, 3 comma 5.5, 4 comma 5, 4 comma 5.5, 5 comma 4.5, 6 comma 3.5, 7 comma 2, 8 comma 1, and 9 comma 0.5
Which of the following describes the pattern of association for the scatter plot?
There is a weak, positive linear association.
There is a weak, negative linear association.
There is a strong, positive nonlinear association.
There is a strong, negative nonlinear association.
Question 5(Multiple Choice Worth 2 points)
(Similar Triangles MC)
Triangle ABC ~ triangle DEF.
triangle ABC with side AB labeled 11, side CA labeled 7.6 and side BC labeled 7.9 and a second triangle DEF with side DE labeled 2.2
Determine the measurement of FD.
FD = 1.52
FD = 1.58
FD = 1.1
FD = 5.5
Question 6(Multiple Choice Worth 2 points)
(Slope MC)
What is the slope of the line that contains the points (−3, −1) and (3, −10)?
Undefined
0
negative two thirds
negative three halves
Question 7(Multiple Choice Worth 2 points)
(Experimental Probability MC)
An experiment is conducted with a coin. The results of the coin being flipped twice 200 times is shown in the table.
Outcome Frequency
Heads, Heads 40
Heads, Tails 75
Tails, Tails 50
Tails, Heads 35
What is the P(No Heads)?
85%
75%
50%
25%
Question 8(Multiple Choice Worth 2 points)
(Dilations MC)
Triangle ABC is dilated to produce triangle A′B′C′.
Graph of a triangle ABC with vertices at A 10 comma 2, B 18 comma 2, C 18 comma 10. Triangle A prime B prime C prime with vertices at A prime 5 comma 1, B prime 9 comma 1, C prime 9 comma 5.
Determine the scale factor used to create the image.
one fourth
one half
2
4
The slope of the line is -4, which means that the swimmer will complete 4 laps every minute. For 5 weeks they have the same amount of money. The direction is 270° clockwise rotation. The pattern of scatter plot is that there is a weak, negative linear association. The measurement of FD = 1.52. The slope of the line is negative three halves. The probability of No Heads is 25%. The scale factor is one half. The correct answers are C), B), A), B), A), D), D) and B).
The slope of the line is the change in y divided by the change in x, which represents the rate of change of the line. In this case, the slope is negative 4, which means that for every minute that passes, the number of laps remaining decreases by 4. So, the swimmer completes 4 laps every minute.
To find the point at which the two savings accounts have the same amount of money, we need to set the two equations equal to each other and solve for x
10x + 25 = 5x + 50
5x = 25
x = 5
So, after 5 weeks, the two siblings will have the same amount of money saved.
The direction of rotation can be determined by looking at the relative positions of the vertices of the original polygon and its image. In this case, the vertices of the image are in quadrant 1, while the vertices of the original polygon are in quadrant 2. This means that the image has been rotated counterclockwise. Additionally, we can see that the image has been rotated by 90 degrees, so the angle of rotation is 90 degrees counterclockwise.
The scatter plot shows a general trend of decreasing cost per cupcake as the number of cupcakes in an order increases. However, there is a fair amount of variability in the data, so the association between the two variables is weak. Additionally, the association is negative, as the cost per cupcake decreases as the number of cupcakes in an order increases.
Similar triangles have proportional side lengths, so we can set up a proportion using corresponding side lengths of the two triangles
AB/DE = BC/EF = CA/FD
Plugging in the known values, we get
11/2.2 = 7.9/EF = 7.6/FD
Solving for FD, we get
FD = (7.6 * 2.2)/11 = 1.52
So, FD has a length of 1.52 units.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula
slope = (y2 - y1)/(x2 - x1)
Plugging in the given values, we get
slope = (-10 - (-1))/(3 - (-3)) = -9/6 = -3/2
So, the slope of the line is negative three halves.
The probability of getting no heads in two flips can be found by adding the frequencies of the outcomes where no heads occur (Tails, Tails) and (Tails, Heads) and dividing by the total number of trials
P(No Heads) = (50 + 35)/200 = 85/200 = 0.425 = 42.5%
So, the probability of getting no heads is 42.5%, which is equivalent to 0.425.
Dilations involve multiplying the coordinates of each vertex by a scale factor. To find the scale factor used in this dilation, we can compare the corresponding side lengths of the original triangle and its image. In this case, we can see that the sides of the image are half as long as the corresponding sides of the original triangle. So, the scale factor used to create the image is one half.
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Please help
Question in image
Answer:
55.5
Step-by-step explanation:
Using the Tangent and Intersected Chord Theorem we know that since the line is tangent to the circle, it will be half of the arc that surrounds the angle. Becuase the arc is 111, dividing it by 2 will give us 55.5
Question 1
Company X tried selling widgets at various prices to see how much profit they would make. The following table shows the widget selling price, x, and the total profit earned at that price, y. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the profit, to the nearest dollar, for a selling price of 7.75 dollars.
Question 2
A tennis ball is dropped from a certain height. Its height in feet is given by h(t)=-16t^2+14 where t represents the time in seconds after launch. What is the ball’s initial height?
The quadratic regression equation is y = -140.61x² + 2,954.23x - 7,512.85 and the ball's initial height is 14 feet.
Writing the quadratic regression equationGiven the set of data
Using a graphing tool, we have
C = -7,512.85B = 2,954.23A = -140.61A quadratic regression equation is represented as
y = Ax² + Bx + C
So, we have
y = -140.61x² + 2,954.23x - 7,512.85
When the selling price is 7.75, we have
y = -140.61(7.75)² + 2,954.23(7.75) + -7,512.85
Evaluate
y = 6937
The initial heightThe ball's initial height is the height when t = 0, which means we need to evaluate the function h(0).
h(0) = -16(0)^2 + 14
h(0) = 0 + 14
h(0) = 14
Therefore, the ball's initial height is 14 feet.
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Directions: Read the scenario below and solve. Show your
work.
If given x > 0 and y> 0, in which quadrant or axis will each
ordered pair described below lie? Explain your answer.
a. (-x, y)
b. (-x, 0)
c. (x, -y)
d. (0. y)
The quadrant or axis for each of the given ordered pairs is:
a. (-x, y) - second quadrant
b. (-x, 0) - X-axis
c. (x, -y) - fourth quadrant
d. (0, y) - Y-axis
How to determine the quadrantsa. (-x, y):
As the x-coordinate is negative (-x), and the y-coordinate is positive (y), the ordered pair (-x, y) will lie in the second quadrant.
b. (-x, 0):
The x-coordinate being negative (-x), and the y-coordinate 0 renders that the ordered pair (-x, 0) lies on the x-axis. This horizontal axis records an unchanging value for y: zero.
c. (x, -y):
The x-coordinate here is a positive value (x), and the y coordinate a negative one (-y); it implies that the ordered pair (x, -y) lies within the fourth quadrant.
d. (0, y):
In this case, the x-coordinate is 0 and the y-coordinate is positive (y); therefore, the ordered pair (0, y) has its place on the y-axis. The y-axis is the vertical line on which x retains a permanent numerical value of zero.
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please answer ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
(a) Lena got 33 more
(b) Last one
I need help on this
Answer:
1.5=slope
Step-by-step explanation:
To do this, we need to solve the slope.
We will use rise/run
0-3=-3
0-2=-2
-3/-2=1.5
Based only on the information given in
theorems or postulates could be given as reasons why AHIJKLM?
Check all that apply.
H
A. LL
L
a
K
B. AAS
C. ASA
D. LA
☐E. HA
OF. HL
MA
The congruency rules which satisfy the given triangles are (B) AAS and (D) HA.
What is triangle congruency?
Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.
Slide, twist, flip, and turn these triangles to create an identical appearance.
If two triangles meet all 5 requirements for congruence, then they are congruent.
They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS). (RHS).
So, according to the given, we can observe that:
2 pairs of angles are congruent one pair of which is 90°.
And 1 pair of sides are congruent.
Then, the rules that satisfy here will be:
AAS and HA
Therefore, the congruency rules which satisfy the given triangles are (B) AAS and (D) HA.
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Complete question:
Based only on the information given in the diagram, which congruence theorems or postulates could begin as reasons why HIJ = KLM?
The figure below shows roads near a pond. Each segment of the triangle represents a road or a path, except AB which represents the distance across the pond. Are the two triangles similar?
Answer:
Yes, triangles ABC and DEC are similar by AA. Angles ABC and DEC are congruent, and angles ACB and DCE are congruent.
3. Set A has a standard deviation of 6. Set B has a standard deviation of 9. Based on
this information, which of the following statements must be true?
A) The range for set A and set B is the same.
B) Set A is larger than set B.
3
C) The mean of set B is 1.5 greater than the mean of set A.
D) The data in set A varies less than the data in set B.
The statement that is true about standard deviation is
Option D is the correct answer.
We have,
Standard deviation is a measure of how spread out the data is in a set.
A smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation indicates that the data points are more spread out from the mean.
Since the standard deviation of set A is 6 and the standard deviation of set B is 9, we can conclude that the data in set A varies less than the data in set B.
So,
The data in set A varies less than the data in set B.
Thus,
The statement that is true about standard deviation is
The data in set A varies less than the data in set B.
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The statement that is true about standard deviation is
Option D is the correct answer.
We have,
Standard deviation is a measure of how spread out the data is in a set.
A smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation indicates that the data points are more spread out from the mean.
Since the standard deviation of set A is 6 and the standard deviation of set B is 9, we can conclude that the data in set A varies less than the data in set B.
So,
The data in set A varies less than the data in set B.
Thus,
The statement that is true about standard deviation is
The data in set A varies less than the data in set B.
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How to draw a quilt of isosceles triangular
The creation of an isosceles triangle quilt can only be achieved through a number of discreet steps:
The StepsInitially, select the bespoke size of both individual triangles and the full-scale length and breadth of the snug.
Subsequently, draft a lattice on either a sheet of paper or digital drafting software, with each square serving as a single triangular unit.
Commencing your task from the bottom row, resonate along the equidistant bases while drawing with precision to ensure an immaculate line-up.
Then, for the succeeding section, diverge by slightly altering the position of the point of each triangle in accordance with the intermediary gap that exists between two triangles below it.
Continue repeating this pattern while constructing rows, enveloping further ground until fully complete coverage has been ensured.
Last but not least, rigorously maintain accuracy by exploiting straight edges strategically laid beside precise measuring instruments.
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4X Minus 3y Equal 21
Step-by-step explanation:
The given equation is:
4x - 3y = 21
To solve for y, we can rearrange the equation as follows:
4x - 21 = 3y
Dividing both sides by 3, we get:
y = (4x - 21) / 3
Therefore, the solution to the equation is:
y = (4x - 21) / 3
Scarlett Squirrel teaches a hula dancing class to young squirrels.
14
1414 squirrels showed up to class on Monday,
10
1010 squirrels on Tuesday,
8
88 squirrels on Wednesday,
10
10squirrels on Thursday, and
12
12squirrels on Friday.
Find the mean number of squirrels.
Answer:
10.8
Step-by-step explanation:
14+10+8+10+12
_______________
5
= 54/5
= 10.8
Posted a image so that you can see it
The missing values are b = 4.37, C = 11° and A = 134°
Given is a triangle, we need to find the missing lengths and angles,
So,
Using the cosine rule,
b² = a²+c² - 2ac Cosb
b = √4²+7²-2(4)(7)cos35°
b = √16+49-45.87
b = √19.13
b = 4.37
Now, using the sine rule,
Sin C / 7 = Sin 35° / 4.37
C = 11°
Applying the angle sum property of triangles,
A = 180°-(11°+35°)
A = 134°
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At a college financial aid office, students who applied for a scholarship were classified according to their class rank: Fr = freshman, So = sophomore, Jr = junior, Se = senior. Construct a frequency distribution for the data.
Fr Fr So Jr Se
Se Fr Jr Fr Fr
Fr Fr So So Fr
Jr Se Se Se Jr
Jr So Fr So Jr
Fr So Jr Se Se
Answer:
Class Rank | Frequency
--- | ---
Fr | 7
So | 3
Jr | 4
Se | 6
Given this equation what is the value of x at the indicated point
Answer:
y = 4
Step-by-step explanation:
[tex]y = -3*-2 - 2\\y = 4[/tex]
What is the side length
Check the picture below.
Need help will give brainliest and 5 stars!
For this graph, for each vertical asymptote, write down the two limits that describe the graph of the function near the asymptote.
The limits on the vertical asymptotes of the function are given as follows:
lim x→6- f(x) = ∞
lim x→6+ f(x) = - ∞
lim x→2- f(x) = ∞
lim x→2+ f(x) = - ∞
lim x→6- f(x) = - ∞
lim x→6+ f(x) = ∞
What are a function's vertical asymptotes?The values of x that are outside of the domain—in a fraction, the zeroes in the denominator—are the vertical asymptotes.
When a graph reaches its vertical asymptotes, it just approaches the point rather than crossing it.
The limits on the vertical asymptotes of the function are given as follows:
lim x→6- f(x) = ∞
lim x→6+ f(x) = - ∞
lim x→2- f(x) = ∞
lim x→2+ f(x) = - ∞
lim x→6- f(x) = - ∞
lim x→6+ f(x) = ∞
The vertical asymptotes are then provided as x = -6, x = -2, and x = 2.
Each asymptote has limits to the left (shown by the minus sign) and the right (shown by the plus sign).
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what is the length of a scaled drawing with a width of 9cm and the scale factor 3/4?
The length of a scaled drawing with a width of 9cm and the scale factor 3/4 s 6.75 cm
Calculating the length of a scaled drawingFrom the question, we have the following parameters that can be used in our computation:
Width = 9cm
Scale factor = 3/4
Using the above as a guide, we have the following:
Length of a scaled drawing = Width * Scale factor
Substitute the known values in the above equation, so, we have the following representation
Length of a scaled drawing = 9 * 3/4
Evaluate
Length of a scaled drawing = 6.75
Hence, the length of a scaled drawing is 6.75 cm
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12.
What is the product of
3 and 10?
Answer:
Any number multiplied by 10 equals to the number and a 0 at the end
Therefore 3×10=3
Express as a product. 1+2cos a
Answer:
Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).
1 + 2cos a = 2(cos a/2 + 1)
Step-by-step explanation:
We can use the trigonometric identity:
cos 2a = 1 - 2 sin^2 a
to rewrite 1 + 2cos a as:
1 + 2cos a = 1 + 2(1 - sin^2 a/2)
= 1 + 2 - 2(sin^2 a/2)
= 3 - 2(sin^2 a/2)
Now, using another trigonometric identity:
sin a = 2 sin(a/2) cos(a/2)
we can rewrite sin^2 a/2 as:
sin^2 a/2 = (1 - cos a)/2
Substituting this into the expression for 1 + 2cos a, we get:
1 + 2cos a = 3 - 2((1 - cos a)/2)
= 3 - (1 - cos a)
= 2 + cos a
Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).
1 + 2cos a = 2(cos a/2 + 1)
HELLPPPP !!!! i need help with the answer I'm stuck!
Answer:
1. f(x)= -2x^2-12x-19
2. f(x)= 2x^2+12x+17
3. f(x)= -2x^2+12x-17
4. f(x)= 2x^2-12x+17
Step-by-step explanation:
Hope this helps!
Answer: f(x)=-2x^2+12x-17 is the 3rd picture (vertex at (3,1))
f(x)=2x^2-12x+17 is the 4th picture (vertex at (3,-1))
f(x)=2x^2+12x+17 is the 2nd picture (vertex at (-3,-1))
f(x)=2x^2+12x-17 does not correlate to a picture.
f(x)=-2x^2-12x-19 is the 1st picture (vertex at (-3,-1))
Suppose Patrick Goldsmith deposited $1000 in an account that earned simple interest at an annual rate of 10% and left it there for 5 years. At the end of the 5 years, Patrick deposited the entire amount from that account into a new account that earned 10% compounded quarterly. He left the money in this account for 5 years. How much did he have after the 10 years? (Round your answer to the nearest cent.)
Answer:
Step-by-step explanation:
After 5 years at a simple interest rate of 10%, Patrick would have earned $500 in interest ($1000 x 10% x 5 years). So at the end of the 5 years, he would have $1500 in the account.
If this entire amount is deposited into a new account that earns 10% compounded quarterly, we need to determine the quarterly interest rate first.
The quarterly interest rate is (1 + 0.10/4)^4 - 1 = 0.025 (rounded to three decimal places).
After 10 years (or 40 quarters) at a quarterly interest rate of 0.025, the compounded amount is:
$1500 x (1 + 0.025)^40 = $4045.56
Therefore, Patrick would have $4045.56 in the account after 10 years when rounding to the nearest cent.
Hope that Helps :)
Cassie uses 1 quart cranberry juice, 1/2 gallon ginger ale, and 1 1/2 pint orange juice to make friut punch .How many 6- ounce servings can she make
She can make 20 6-ounce servings to make fruit punch
How to determine this
Cassie uses 1 quart cranberry juice,
1/2 gallon ginger ale,
1 1/2 pint orange juice.
1 quart of cranberry juice when converted to ounce
1 quart = 32 ounces
1/2 gallon of ginger ale when converted to ounce
1 gallon = 128 ounces
1/2 gallon = 128/2
1/2 gallon = 64 ounces
1 1/2 pint orange juice to make fruit punch
1 pint = 16 ounces
1 1/2 pint = 16 + 16/2 ounces
= 16 + 8
= 24 ounces
How many 6-ounces servings can she make
32 + 64 + 24
= 120 ounces
6-ounces that can be made
= 120 ounces/6 ounces
= 20 servings
Therefore, 20 6-ounce servings can be make for fruit punch
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