The solution is; 10 days for Soccer and, 14 days for Baseball camp, are needed to run each of the camps sessions .
Here, we have,
given that,
The Parks and Recreation Department is planning to host sports camps for students during the summer.
Option 1 is to have 8 Soccer and 1 Baseball camp sessions that would last 94 days altogether.
Option 2 has 3 Soccer and 5 Baseball camp sessions that would last 100 days.
now, let,
x days for Soccer and, y days for Baseball camp, are needed to run each of the camps sessions .
then, we have,
8x + y = 94 .....1
3x+ 5y = 100 .....2
solving we get,
equation 1 => 40x + 5y = 470
now, subtracting, we get,
37x = 370
so, x = 10
now, solving we get,
y = 14
Hence, The solution is; 10 days for Soccer and, 14 days for Baseball camp, are needed to run each of the camps sessions .
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Amelia borrowed £1600 at a simple interest rate of
8% per year.
After a certain number of years, she owes a total of
£2496 on this loan.
How many years have passed since she took out
the loan?
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2496\\ P=\textit{original amount deposited}\dotfill & \pounds1600\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases} \\\\\\ 2496 = 1600[1+(0.08)(t)]\implies \cfrac{2496}{1600}=1+0.08t\implies \cfrac{39}{25}=1+0.08t \\\\\\ \cfrac{39}{25}-1=0.08t \implies \cfrac{14}{25}=0.08t\implies \cfrac{14}{25(0.08)}=t\implies 7=t[/tex]
Find the length of side x to the nearest tenth.
Answer: 7.8
Step-by-step explanation: Identify the triangle as a 45-45-90 triangle.
Recognize that the sides of a 45-45-90 triangle are in a ratio of 1:1:√2.
Find the length of the hypotenuse of the triangle. In this case, the hypotenuse is 11 units.
Divide the length of the hypotenuse by √2 to find the length of the side opposite the 45-degree angle. In this case, the length of side x is 11/√2 = 7.77 units.
Round the length of side x to the nearest tenth. In this case, the length of side x is 7.8 units.
Answer:
= 10.4
Step-by-step explanation:
Here given is the right-angled triangle
For angle: = 60º
Perpendicular: = 9
Hypotenuse: =
Now using the trigonometry formula:
= /
sin 60º = 9/
3√2 = 9/
= 18/3√
= 10.4(rounded to the nearest tenth)
Therefore required length is = 10.4
The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
a. bus
b. car
c. subway
d. train
Answer: C
Step-by-step explanation:
For box and whiskers plot the box is where the majority of the data is. the whiskers(the lines on both sides will tell you where the range of numbers lie)
The middle line in the box is the median number.
The question is worded oddly where they want least likely to be more than 30 which means which one will have less than 30. (Double negative question)
You want the majority of the data to be less than 30, which is subway. C
Tanker trucks are designed to carry huge quantities of gasoline from refineries to filling stations. A factory that manufactures the tank of the trucks claims to manufacture tanks with a capacity of 8550 gallons of gasoline. The actual capacity of the tanks is normally distributed with mean μ = 8544 gallons and standard deviation σ = 12 gallons. A simple random sample of n = 20 tanks will be selected. Find the z-score corresponding to a sample mean capacity for 20 tanks of 8550. Round your answer to three decimal places. (Example: 0.398)
The z-score corresponding to a sample mean capacity for 20 tanks of 8550 is 2.238.
To find the z-score corresponding to a sample mean capacity for 20 tanks of 8550, we need to use the formula for the z-score:
z = (x - μ) / (σ / √n)
Where:
x = sample mean capacity
μ = population mean capacity
σ = population standard deviation
n = sample size
Given:
x = 8550, μ = 8544, σ = 12 and n = 20
Substituting these values into the formula:
z = (8550 - 8544) / (12 / √20)
z = 6 / (12 / √20)
z = 6 / (12 / 4.472)
z = 6 / 2.683
z = 2.238
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Task Card #9
Q
U
Solve for x
|
(4x-10)°
K
Angle Relationship?
What is the m
Based on the information provided, we have an angle labeled as (4x-10)° and another angle labeled as K. It seems like we need to determine the relationship between these angles and find the value of x.
To determine the relationship between the angles, we need more context or information about the specific geometric configuration or properties mentioned in the task card. Without additional information, it is not possible to determine the relationship between (4x-10)° and K.
If you can provide further details or a description of the geometric setup or any additional instructions related to the angle relationship, I'll be glad to help you further.
PLEASE HELP ITS GEOMETRY
Answer:
[tex]slope_{UF}[/tex] = - [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
calculate slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = U (3, - 5 ) and ( x₂, y₂ ) = F (- 1, - 4 )
m = [tex]\frac{-4-(-5)}{-1-3}[/tex] = [tex]\frac{-4+5}{-4}[/tex] = [tex]\frac{1}{-4}[/tex] = - [tex]\frac{1}{4}[/tex]
Find the area of a regular dodecagon (12 -gon) with a
side length of 9 inches. Round your answer to the
nearest hundredth.
The area is about
square inches.
Answer:
906.89 in²
Step-by-step explanation:
A regular dodecagon is a specific type of 12-sided polygon where all sides and angles are equal.
The formula for the area of a regular polygon is:
[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\cdot s\cdot a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}[/tex]
We know that the number of sides is 12 and that the length of one side is 9 inches, so in order to calculate the area, we first need to find the apothem.
The formula for the apothem of a regular polygon is:
[tex]\boxed{\begin{minipage}{6cm}\underline{Length of apothem}\\\\$a=\dfrac{s}{2 \tan\left(\frac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $a$ is the apothem.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]
Substitute s = 9 and n = 12 into the apothem formula, and solve for a:
[tex]a=\dfrac{9}{2 \tan\left(\frac{180^{\circ}}{12}\right)}[/tex]
[tex]a=\dfrac{9}{2 \tan\left(15^{\circ}\right)}[/tex]
[tex]a=\dfrac{9}{2 \left(2-\sqrt{3}\right)}[/tex]
[tex]a=\dfrac{9}{4-2\sqrt{3}}[/tex]
[tex]a=\dfrac{9}{4-2\sqrt{3}}\cdot \dfrac{4+2\sqrt{3}}{4+2\sqrt{3}}[/tex]
[tex]a=\dfrac{36+18\sqrt{3}}{4}[/tex]
[tex]a=\dfrac{18+9\sqrt{3}}{2}[/tex]
Now we have calculated the apothem, substitute this along with n = 12 and s = 9 into the area of a polygon formula
[tex]A=\dfrac{n \cdot s \cdot a}{2}[/tex]
[tex]A=\dfrac{12 \cdot 9 \cdot \frac{18+9\sqrt{3}}{2}}{2}[/tex]
[tex]A=\dfrac{108 \cdot \frac{18+9\sqrt{3}}{2}}{2}[/tex]
[tex]A=54 \cdot \dfrac{18+9\sqrt{3}}{2}}[/tex]
[tex]A=27\cdot (18+9\sqrt{3}})[/tex]
[tex]A=486+243\sqrt{3}[/tex]
[tex]A=906.89\; \sf in^2\;(nearest\;hundredth)[/tex]
Therefore, the area of a regular dodecagon with a side length of 9 inches is 906.89 in² (nearest hundredth).
Note: Please see the attached image for confirmation of the area using a graphic calculator.
a straight line has an equation given by:
2y= 4x-5.
write down the gradient of the straight line
Step by Step Solution/ just copy and paste but if this is a test, the answer is 2.000
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2*y-(4*x-5)=0
STEP
1
:Equation of a Straight Line
1.1 Solve 2y-4x+5 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 2y-4x+5 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is -5/2 so this line "cuts" the y axis at y=-2.50000
y-intercept = -5/2 = -2.50000
Calculate the X-Intercept :
When y = 0 the value of x is 5/4 Our line therefore "cuts" the x axis at x= 1.25000
x-intercept = 5/4 = 1.25000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -2.500 and for x=2.000, the value of y is 1.500. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 1.500 - (-2.500) = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 4.000/2.000 = 2.000
Geometric figure: Straight Line
Slope = 4.000/2.000 = 2.000
x-intercept = 5/4 = 1.25000
y-intercept = -5/2 = -2.50000
I need helping finding the equation of the ellipse please.
Turn me into a superhero
If a cyclist traveled 45 miles in 2 1/2 hours. How long would it take her to travel 153 miles?
Answer: it would take the cyclist 8.5 hours to travel 153 miles.
Step-by-step explanation: We can use proportions to solve this problem.
Let's define:
x = the time it would take for the cyclist to travel 153 miles.
Using proportions, we can set up the following equation:
45 miles / 2.5 hours = 153 miles / x
We can then cross-multiply and solve for x:
45 * x = 2.5 * 153
45x = 382.5
x = 382.5 / 45
x = 8.5
If fifteen cubed shape gift boxes can be covered by roll of wrapping paper, show by means of calculation that the area is 3.6m if the length is 20 cm
The total area covered by the roll of wrapping paper is 3.6 square meters.
To calculate the total area covered by the wrapping paper, we need to find the surface area of each cube and then multiply it by the number of cubes.
The formula for the surface area of a cube is:
Surface Area = 6 * (side length)^2
Given that the length of each side of the cube is 20 cm (which is equal to 0.2 meters), we can substitute this value into the formula:
Surface Area = 6 * (0.2)^2
Surface Area = 6 * 0.04
Surface Area = 0.24 square meters
Now, we know that 15 cubes can be covered by the roll of wrapping paper. Therefore, the total area covered by the wrapping paper is:
Total Area = Surface Area * Number of Cubes
Total Area = 0.24 * 15
Total Area = 3.6 square meters
Therefore, the total area covered by the roll of wrapping paper is 3.6 square meters.
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From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of 4 pieces of fruit is selected. If X is the number of oranges and Y is the number of apples in the sample, find
(a)the joint probability distribution of X and Y;
(b)P[(X,Y) € A), where A is the region that is given by ((a.v) |a+y <2).
(a) The joint probability distribution of X and Y is 3/70.
(b) The value of P[(X,Y) € A), where A is the region that is given is 3/35.
What is the joint probability distribution of X and Y?(a) To find the probabilities, we consider the total number of ways to select 4 fruits out of 8:
Total number of ways to select 4 fruits out of 8 = C(8, 4) = 70
The probabilities for each combination of X and Y are as follows:
P(X = 0, Y = 0) = C(3, 0) * C(2, 0) * C(3, 4) / 70
P(X = 0, Y = 0) = 1 / 70
P(X = 0, Y = 1) = C(3, 0) * C(2, 1) * C(3, 3) / 70
P(X = 0, Y = 1) = 2 / 70
P(X = 1, Y = 0) = C(3, 1) * C(2, 0) * C(3, 3) / 70
P(X = 1, Y = 0) = 3 / 70
P(X = 1, Y = 1) = C(3, 1) * C(2, 1) * C(3, 2) / 70
P(X = 1, Y = 1) = 18 / 70
P(X = 2, Y = 0) = C(3, 2) * C(2, 0) * C(3, 2) / 70
P(X = 2, Y = 0) = 9 / 70
P(X = 2, Y = 1) = C(3, 2) * C(2, 1) * C(3, 1) / 70
P(X = 2, Y = 1) = 18 / 70
P(X = 3, Y = 0) = C(3, 3) * C(2, 0) * C(3, 1) / 70
P(X = 3, Y = 0) = 3 / 70
The joint probability distribution of X and Y is as follows:
X\Y 0 1
0 1/70 2/70
1 3/70 18/70
2 9/70 18/70
3 3/70 0
(b) P[(X,Y) ∈ A], where A is given by ((a + v) | a + y < 2):
From the joint probability distribution table, we can see that the combinations (0, 0), (0, 1), and (1, 0) satisfy this condition.
P[(X, Y) ∈ A] = P[(0, 0)] + P[(0, 1)] + P[(1, 0)] = 1/70 + 2/70 + 3/70
P[(X, Y) ∈ A] = 6/70 or 3/35
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What is the quadratic equation??
Plsss reply I’ll mark as brainliest
Hello !
1. A quadratic equation results in the form: ax² + bx + c
2. Calculate the discriminant: Δ = b² - 4ac
3. Calculate x with the dicriminant: (-b ± √Δ) / 2a
Example:
3x² + 7x - 2 = 0 is a quadratic equation.
x = (-b ± √(b² - 4ac)) / 2a
= (-7 ± √(7² - 4*3*(-2))) / (2*3)
= (-7 ± √73)/6
There is a jar in the cabinet by the refrigerator. If Kenna pours 114 ounces of water into the jar 3 times to fill it, how many quarts of water does it take to fill the jar? (Round to then nearest whole number)
Answer:
Since 1 fluid ounce is equal to 0.03125 quarts, we can convert the volume of water poured into the jar from ounces to quarts:
114 ounces x 0.03125 quarts/ounce = 3.5625 quarts
Therefore, Kenna pours 3 x 3.5625 = 10.6875 quarts of water to fill the jar three times. Rounding to the nearest whole number, we get 11 quarts.
So it takes 11 quarts of water to fill the jar.
express cos A as a fraction in simplest terms
12/13 is the value of cosA is in the triangle ABC
ABC is a right angle triangle
Angle B has a angle of 90 degrees
We know that the cosine function is a ratio of adjacent side and hypotenuse
The adjacent side of angle A is AB which we have to find
hypotenuse is 26
Cos A =AB/26
Let us find AB by using pythagoras theorem
10²+AB²=26²
100+AB²=676
Subtract 100 from both sides
AB²=576
Take square root on both sides
AB=√576
=24
Now plug in this value in cosA
CosA = 24/26
=12/13
Hence, the value of cosA is 12/13 in the triangle ABC
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Can be written in Simplest form
Answer:
8[tex]\sqrt[3]{2}[/tex]
Step-by-step explanation:
The cube root of -2 to the power of 10 is;
(-2)^10=2^10
2^10=(2^3)*(2^3)*(2^3)*2
You can factor out 2^3=8 of the cube root
So you get 8 times the cube root of 2
What is the vector shown in component form?
The vector shown in component form is (-4, -3)
We have to find the vector which is shown in the component form
To find this vector we have to find the difference of tail and head
Tail has coordinates (1, 2)
Head has coordinates (-3, -1)
We have to subtract (-3, -1) from (1, 2)
(-3, -1)-(1,2)
We have to do this by subtracting x coordinates and y coordinates
(-3-1, -1-2)
(-4, -3)
Hence, (-4, -3) is the vector shown in component form
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An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The
equation 200e0.08350 represents the situation, where t is the number of years the money has been invested. About
how long has the money been invested? Use a calculator and round your answer to the nearest whole number.
O 5 years
O 7 years
O 19 years
O 22 years
abs(2x+5)+abs(3x-1)=10
Answer:
Step-by-step explanation:
x=6/5,−4
Decimal Form:
x=1.2,−4
Mixed Number Form:
x=1 1/5,−4
What is the remainder when y? + 5 is divided by * + 1?
Answer:
[tex]\frac{6}{x+1}[/tex]
Step-by-step explanation:
I learned this like a month ago so I have notes abt it if you don't understand how it works. Just lmk if you need them
order from least to greatest -7, -8, -2, 6, | -11 |, - 11, -9, 4, 5
The given numerical data should be ordered from least to greatest as follows;
-11, -9, -8, -7, -2, 4, 5, 6, |-11|.
What is a rational number?In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals.
In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1).
Next, we would order or sort the given numerical data from least to greatest as follows;
-11, -9, -8, -7, -2, 4, 5, 6, |-11|.
Note: |-11| is an absolute value that equals to 11.
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what should be subtracted from 7/12+7/8 to obtain the multiplicated inverse of (4/3-4/9)
To find the subtracted value, we need to calculate the multiplicative inverse of (4/3 - 4/9) and then subtract it from the sum of 7/12 and 7/8.
First, let's find the multiplicative inverse of (4/3 - 4/9):
Multiplicative inverse = 1 / (4/3 - 4/9)
To simplify the expression, we need a common denominator:
Multiplicative inverse = 1 / ((12/9) - (4/9))
= 1 / (8/9)
= 9/8
Now, we need to subtract the multiplicative inverse from the sum of 7/12 and 7/8:
Subtracted value = (7/12 + 7/8) - (9/8)
To perform this calculation, we need a common denominator:
Subtracted value = (7/12 * 2/2 + 7/8 * 3/3) - (9/8)
= (14/24 + 21/24) - (9/8)
= 35/24 - 9/8
To simplify further, we need a common denominator:
Subtracted value = (35/24 * 1/1) - (9/8 * 3/3)
= 35/24 - 27/24
= 8/24
= 1/3
Therefore, subtracting 1/3 from the sum of 7/12 and 7/8 will give you the multiplicative inverse of (4/3 - 4/9).
Use limits to find the area of the region between the graph of y=x² +1
and the x-axis on the interval [2, 4], or f(x²+1) dx
Answer: To find the area of the region between the graph of y = x^2 + 1 and the x-axis on the interval [2, 4], we can integrate the function f(x) = x^2 + 1 with respect to x over the given interval. The definite integral represents the area under the curve between the specified x-values. Here's how to calculate it using integration:
∫[2,4] (x^2 + 1) dx
To integrate this function, we apply the power rule for integration. The power rule states that the integral of x^n with respect to x is (x^(n+1))/(n+1), where n is any real number except -1.
∫(x^2 + 1) dx = [(x^3)/3 + x] + C
Now, we can evaluate the definite integral over the interval [2, 4]:
[(4^3)/3 + 4] - [(2^3)/3 + 2]
= (64/3 + 4) - (8/3 + 2)
= (64/3 + 12/3) - (8/3 + 6/3)
= (76/3) - (14/3)
= 62/3
Therefore, the area of the region between the graph of y = x^2 + 1 and the x-axis on the interval [2, 4] is 62/3 square units.
Step-by-step explanation:
A car owner pays an annual premium of $780 for automobile insurance, including liability coverage of up to $100,000. The car owner pays this for five years without needing to file a single claim. Then the car owner causes an accident for which the other driver is claiming $32,000 in damages. How much more expensive were the costs of the accident than what the car owner paid in premiums?
$3,900
$28,100
$35,900
$100,000
The correct answer is $28,100.
To calculate the difference between the costs of the accident and the premiums paid by the car owner, let's break down the expenses step by step:
(1) Annual Premium: The car owner pays an annual premium of $780 for automobile insurance. Over five years, the total premium paid is $780 * 5 = $3,900.
(2) Liability Coverage: The liability coverage provided by the insurance is up to $100,000. However, the other driver is claiming $32,000 in damages. Therefore, the insurance will cover the full amount of $32,000.
(3) Difference in Costs: To find the difference between the costs of the accident and the premiums paid, we subtract the insurance coverage from the total premium paid. In this case, the difference is $32,000 - $3,900 = $28,100.
Therefore, the costs of the accident were $28,100 more expensive than what the car owner paid in premiums.
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help meeeeeeeeeeeeeeeeeeeee...e
Answer:
True, True, False
Step-by-step explanation:
1. 8 ≥ 5-1 Is correct
2. 8 ≥ 5-4 is correct
3. 8 ≥ 5-(-4) is not correct
Answer:
x = 1 makes the inequality true
x = 4 makes the inequality true
x = -4 makes the inequality false
Step-by-step explanation:
We can determine whether x = 1, x = 4, and x = -4 makes the inequality by plugging in 1, 4, and -4 for x and seeing whether the inequality still holds true:
Step 1: Plugging in 1 for x:
8 ≥ 5 - 1
8 ≥ 4
Because 8 is greater than 4, x = 1 makes the inequality true.
Step 2: Plugging in 4 for x:
8 ≥ 5 - 4
8 ≥ 1
Because 8 is also greater than 4, x = 4 also makes the inequality true.
Step 3: Plugging in -4 for x:
8 ≥ 5 - (-4)
8 ≥ 5 + 4
8 ≥ 9
Because 8 is not less than 9, x = -4 makes the inequality false
250 people travelled to a conference either by bus or by train
95 of the people travelled by bus
102 of the 126 people who arrived late travelled by train
use this information ro complete the frequency tree
Answer:
250
/ \
126 124
\ / \
102 24 87 57
/ \ / \ / \
100 6 22 2 40 17
/ / \ / / \ / / \
95 0 5 22 0 20 0 37
The frequency tree shows that 126 people arrived late, and 102 of them travelled by train. This means that 24 people arrived late and travelled by bus. There were a total of 250 people who attended the conference, so 124 people arrived on time. Of the people who arrived on time, 87 travelled by bus and 57 travelled by train.
Answer:
Step-by-step explanation:
The graph (in red) shows the speed (m/s) of a car for 36 seconds.
A triangle has been drawn underneath part of the curve to estimate the distance travelled
between 30 and 36 seconds.
By using an appropriate single trapezium under the first part of the graph, estimate the total
distance travelled by the car in those 36 seconds.
30 T Speed (m/s)
25
20
15
10
5
O
0 5
10
15
20
25
Tirhe (seconds)
30
35
40
4
C Get help
5 -
-Area under a
Template.pdf
Area under a
Template.pdf
Report a mista
Quit assessme
On-screen key
To estimate the total distance traveled by the car in those 36 seconds, we can use the trapezium rule to approximate the area under the curve.
From the graph, we can see that the car's speed is constant between 0 and 30 seconds, and then it starts to decrease. Therefore, we can use a single trapezium to estimate the area under the curve for the first part.
The base of the trapezium is 30 seconds, and the height is the average of the speeds at 0 and 30 seconds. Let's denote the speed at 0 seconds as v0 and the speed at 30 seconds as v30.
The distance traveled in the first part can be estimated as:
Distance = 30 * (v0 + v30) / 2
To get a more accurate estimate, we need the specific values of v0 and v30 from the graph. Please provide the corresponding speed values for 0 and 30 seconds, and I can help you calculate the estimated distance.
a parabola opens upward. the parbola goes through the point (3,-1) and the vertex is at (2,-2) what are the values of h and v
The coordinates of the focus obtained from the vertex form of the equation of the parabola is; (h, v) = (2, -7/4)
What is the vertex form of the equation of a parabola?The vertex form of the equation of a parabola is; y = a·(x - h)² + k
The points on the parabola are;
(3, -1), and (2, -2)
The vertex of the parabola is; (2, -2)
Therefore, we get;
The vertex form of the equation of a parabola is; y = a·(x - h)² + k
Where;
(h, k) = The coordinates of the vertex, therefore;
y = a·(x - 2)² - 2
y + 2 = a·(x - 2)²
The point (3, -1), indicates that we get;
-1 + 2 = a·(3 - 2)²
(-1 + 2)/((3 - 2)²) = 1 = a
The equation of the parabola in focus form is; (x - h)² = 4·p·(y - k)
Therefore; (x - 2)² = 4·p·(y + k)
We get; (x - 2)² = (y + k)
(x - 2)²/(4·p) = y + k
(4·p) = a = 1
p = 1/4
The y-coordinates of the focus, v = -2 + 1/4 = -1 3/4 = -7/4
The coordinates of the focus, (h, v) is therefore;
(h, v) = (2, -7/4)
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What is the approximate value of θ if tan θ = 7/9
Answer:
37.9°-----------------------
Taking the inverse tangent (arctan) of the given ratio 7/9.
Use a calculator or trigonometric table to find:
θ ≈ arctan(7/9)The approximate value of θ is 37.9°.
4. **Suzie makes a purchase of $160 and is charged 7.85% for sales tax. What is the total cost of the purchase if Suzie charges it on a credit
card with a daily interest rate of 0.042% and pays the balance off at the end of 30 days? Round to the nearest cent
Hint: 1st, calculate the total cost of the purchase, which includes the sales tax. It is $160+($160 sales tax). Don't forget to change to
decimal before multiplying.
2nd, what will the interest per day be? You can find this by multiplying 0.042% (change to decimal first) by the total cost of the purchase you
found in 1st step. Now multiply the interest you found by 30 days, and add it to the total cost of the purchase.
a. $172.56
b. $174.73
c. $190.77
d. $200.26
Answer:
First find the sales tax: $160 \times 0.0785 = $12.56.
Then add the sales tax to the price of the purchase to find the total cost: $160 + $12.56 = $172.56.
Next find the daily interest rate: $0.042\% = 0.00042$.
Then multiply the daily interest rate by the total cost to find the interest per day: $0.00042 \times $172.56 = $0.0725752$.
Finally, multiply the interest per day by 30 days to find the total interest and add it to the total cost to find the final answer: $0.0725752 \times 30 = $2.177256 + $172.56 = $174.737256 \approx $174.74.
So the answer is b.