The recipe of the junk calls for 16/7 cups of sugar
How to determine the number of cups of sugar in the recipe?From the question, the given parameters are:
Total number of cups = 8
Let the number of cups of sugar be x and the number of cups of flour be y
So, we have the following equation
x + y = 8
Also, we have:
The recipe uses 1/4 cup more sugar, so the amount of sugar equals half the amount of flour
This means that
(1 + 1/4) * x = 1/2 * y
Evaluate the sum and the products
So, we have
5/4x = 1/2y
Make y the subject
y = 5/2x
Substitute y = 5/2x in x + y = 8
x + 5/2x = 8
Evaluate the sum
3.5x = 8
Divide by 3.5
x = 16/7
Hence, the cups of sugar is 16/7
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Demarcus and Lauren each take out a $90,000 loan for a new condo. Each has to repay the loan in 10 years. Demarcus will pay an interest rate of 2.8% per year. His monthly payments will be $771. Because Lauren has a lower credit score, she will have to pay an interest rate of 3.7% per year. Her monthly payments will be $840. How much more will a $90,000 loan cost Lauren than Demarcus?
The amount that a $90,000 loan cost Lauren than Demarcus will be $8280.
How to calculate the value?From the information, Demarcus and Lauren each take out a $90,000 loan for a new condo and each has to repay the loan in 10 years. It should be noted that 10 years in months will be:
= 10 × 12 = 120 months
The difference in the amount paid as a result of the credit score will be:
= ($840 × 120) - ($771 × 120)
= $100800 - $92520
= $8280
Therefore, the amount is $8280.
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a container holds 2300 ounces fruit punch. A factory places the fruit punch into 32-ounce bottles. How man full Bottles of fruit punch can the factory produce?
find the exact perimeter of hexagon ABCDEF plotted below
The perimeter of the hexagon ABCDEF is 36.01.
Given,
The hexagon ABCDEF
We have given the points:
A(-6, 2), B(1, 5), C(6, 5), D(6, -1), E(1, -3), F(-6, -3)
We have to find the perimeter of hexagon.
Perimeter of hexagon = AB + BC + CD + DE + EF + FA
Now,
Distance formula is as [tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
So,
Distance of AB,A(-6, 2), B(1, 5) : x₁ = 1, x₂ = -6, y₁ = 2, y₂ = 5
[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(1-(-6))^{2} +(5-2)^{2} }[/tex]
=[tex]\sqrt{7^{2} +3^{2} }[/tex]
= [tex]\sqrt{49+9}[/tex]
= √58
= 7.62
Distance of BC,B(1, 5), C(6, 5) : x₁ = 1, x₂ = 6, y₁ = 5, y₂ = 5
[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(6-1)^{2}+(5-5)^{2} }[/tex]
= √5²
= 5
Distance of CD,C(6, 5), D(6, -1) : x₁ = 6, x₂ = 6, y₁ = 5, y₂ = -1
[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(6-6)^{2}+(-1-5)^{2} }[/tex]
= √-6²
= 6
Distance of DE,D(6, -1), E(1, -3) : x₁ = 6, x₂ = 1, y₁ = -1, y₂ = -3
[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(1-6)^{2}+(-3-(- 1))^{2} }[/tex]
= [tex]\sqrt{(-5)^{2} +(-3+1)^{2} }[/tex]
= [tex]\sqrt{25 + 4}[/tex]
= √29
= 5.39
Distance of EF,E(1, -3), F(-6, -3) : x₁ = 1, x₂ = -6, y₁ = -3, y₂ = -3
[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(-6-1)^{2}+(-3-(-3))^{2} }[/tex]
= √-7²
= 7
Distance of FA,F(-6, -3), A(-6, 2) : x₁ = -6, x₂ = -6, y₁ = -3, y₂ = 2
[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(-6-(-6))^{2} +(-3-(2))^{2} }[/tex]
= √-5²
= 5
So, we have
AB = 7.62
BC = 5
CD = 6
DE = 5.39
EF = 7
FA = 5
Now,
Perimeter of hexagon = AB + BC + CD + DE + EF + FA
Perimeter of hexagon= 7.62 + 5 + 6 + 5.39 + 7 + 5
Perimeter of hexagon = 36.01
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Name the property, if any, that is illustrated below
The given expression xy = yx represents the cumulative property of multiplication.
What is cumulative property?If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics. Numerous binary operations share this essential characteristic, and numerous mathematical arguments rely on it.
The given expression is xy = yx.
The expression xy = yx is representing the cumulative property of multiplication. According to this property, the value of the expression will remain the same after the order is changed.
Let x = 5 and y = 10. Now verify the cumulative property of multiplication.
xy = yx
5 x 10 = 10 x 5
50 = 50
Therefore, the given expression xy = yx represents the cumulative property of multiplication.
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When a number is decreased by 20% of itself, the result is 336. What is the number?
The number which is decreased by 20% and result is 336 then number is 420
According to the question, given that
when a number is decreased by 20 % of itself, it became 336
then, the number is :
x - (x ×[tex]\frac{20}{100}[/tex] )= 336
x - [tex]\frac{x}{5}[/tex] = 336
[tex]\frac{5x - x}{5}[/tex] = 336
[tex]\frac{4x}{5}[/tex] = 336
x = [tex]\frac{336 *5}{4}[/tex]
x = 84 * 5
x = 420
Therefore, we get the number is 420
PERCENT INCREASE =(new amount−original amount)/original amount
Some people append 100% at the end of this calculation to stress that it should be stated as a percent since it represents an increase in percentage.
So, as an alternative, here is the formula:
PERCENT INCREASE = (new amount−original amount)/original amount*100%
PERCENT DECREASE=(original amount−new amount)original amount
OR
PERCENT DECREASE=(original amount−new amount)original amount*100%
Both formulas have the following pattern:
PERCENT INCREASE/DECREASE=change in amount /original amount
OR
PERCENT INCREASE/DECREASE=change in amount/ original amount*100%
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Find the savings plan balance after 3 years with an APR of 7% and monthly payments of $100.
The savings plan balance (future value) after 3 years with a 7% APR and monthly payments of $100 is $3,993.01.
What is the future value?The future value is the present value or cash flows compounded at an interest rate for a period.
The future value can be computed using an online finance calculator.
N (# of periods) = 36 months
I/Y (Interest per year) = 7%
PV (Present Value) = $0
PMT (Periodic Payment) = $100
Results:
FV = $3,993.01
Sum of all periodic payments = $3,600 ($100 x 36)
Total Interest = $393.01
Thus, at the end of 3 years, the saving plan balance grew to a future value of $3,993.01.
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This is my question…
Solution
otal number of cCustomer = 11 + 9 + 11 + 5 + 5 + 1 + 3 = 45
Let A denotes the event that the Customer waited for at least 12 minutes
Let B denotes the event that the Customer waited between 8 and 15 minutes
[tex]\begin{gathered} n(A)=5+5+1+3=14 \\ n(B)=11+5=16 \\ n(A\cap B)=5 \end{gathered}[/tex]We want to find
[tex]p(A\cup B)[/tex][tex]\begin{gathered} p(A\cup B)=p(A)+p(B)-p(A\cap B) \\ p(A\cup B)=\frac{14}{45}+\frac{16}{45}-\frac{5}{45} \\ p(A\cup B)=\frac{25}{45} \\ p(A\cup B)=\frac{5}{9} \\ p(A\cup B)=0.556\text{ (to the nearest thousandth)} \end{gathered}[/tex]hus, the probability is 0.556
Option D
use the rectangle diagram at the right.Write and solve an inequality to find the value of x for which the perimeter of the rectangle is less than 120.
The perimeter is the sum of all the sides of a geometric figure, so
[tex]\begin{gathered} (x+4)+x+(x+4)+x<120 \\ x+4+x+x+4+x<120 \\ 4x+8<120 \end{gathered}[/tex]To resolve this inequality you can first subtract 8 from both sides
[tex]\begin{gathered} 4x+8-8<120-8 \\ 4x<112 \end{gathered}[/tex]Then you divide by 4 on both sides of the inequality
[tex]\begin{gathered} \frac{4x}{4}<\frac{112}{4} \\ x<28 \end{gathered}[/tex]Therefore, for the perimeter of the rectangle to be less than 120, its shortest side must measure less than 28.
A theatre has 30 rows of seats there are 22 seats in the first row 26 in the second row 30 in the third row etc how many people will the theatre hold
Using the arithmetic progression, If a theatre has 30 rows of seats there are 22 seats in the first row,26 in the second row, 30 in the third row, then the total number of people that the theatre hold is 2400
The total number of rows = 30
Number of seats in the first row = 22
Number of seats in the second row = 26
Number of seats in the third row = 30
Common difference= Second term - first term
= 26-22
= 4
The given sequence is in arithmetic progression
Sum of n terms = [tex]\frac{n}{2}[2a+(n-1)d][/tex]
Substitute the values in the equation
= [tex]\frac{30}{2}[2(22)+(30-1)4][/tex]
= 15[44+29×4]
= 15[44+116]
= 15×160
= 2400
Hence, using the arithmetic progression, if a theatre has 30 rows of seats and there are 22 seats in the first row,26 in the second row, 30 in the third row, then the total number of people that the theatre hold is 2400
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A zucchini plant in Darnell's garden was 10 centimeters tall when it was first planted. Since then, it has grown approximately 0.5 centimeters per day. a. Write a rule to describe the function. b. After how many days will the zucchini plant be 0.185 meters tall?
a) g(x) = 10 + 0.5x
b) 17 days
Explanations:Let the number of days be represented by x
Let the intial height of the zucchini plant be g₀
g₀ = 10 cm
Size of growth per day = 0.5 cm
Let the growth after x days be represented by g(x)
a) The rule that represents the function is therefore:
g(x) = g₀ + 0.5x
g(x) = 10 + 0.5x
b) After how many days will the Zucchini pant be 0.185 meters tall
That is g(x) = 0.185 meters
since 1 meter = 100 cm
g(x) = 0.185 x 100 cm
g(x) = 18.5 cm
Thereofre substitute g(x) = 18.5 into the equation g(x) = 10 + 0.5x
18.5 = 10 + 0.5x
18.5 - 10 = 0.5x
0.5x = 8.5
x = 8.5 / 0.5
x = 17
The zucchini plant will be 0.185 meters tall after 17 days
solve the inequality and describe the graph of the solution.[tex]4x - 5 \geqslant 7[/tex]
The given expression is :
[tex]4x-5\ge7[/tex]To simplify the expression for x :
Add 5 on both side :
[tex]\begin{gathered} 4x-5+5\ge7+5 \\ 4x\ge12 \end{gathered}[/tex]
Divide the expression by 4 on both side :
[tex]\begin{gathered} 4x\ge12 \\ \frac{4x}{4}\ge\frac{12}{4} \\ x\ge3 \end{gathered}[/tex]Thus : x ≥ 3
The graph is :
Since x is greater than or equal to 3
So, it is closed on 3
Answer :
The graph has a closed circle on 3 and is shaded to the right of the origin
Find 4/9 divided by 7/8 use multiplication to check your result
From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 7.90 m/s and angle of 24.0° below the horizontal. It strikes the ground 5.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical values; use variables only.) xi = yi = (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. vi, x = m/s vi, y = m/s (c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: y0 and t. Assume SI units.) x = m y = m (d) How far horizontally from the base of the building does the ball strike the ground? m (e) Find the height from which the ball was thrown. m (f) How long does it take the ball to reach a point 10.0 m below the level of launching? s
The description of the motion of the ball, which is a projectile are as follows;
(a) The window coordinates are; (0, 138.49)
(b) The x–component is 7.22 m)s
The y–component is -3.22 m/s
(c) The equations for displacement are;
x = 7.22•ty = 3.21•t + 4.91•t²(d) 16.07 m from the base
(e) Height of the ball location before it was thrown is 138.49 meters
(f) Time to reach 10.0 m. is 1.14 s
What is a projectile motion?Projectile motion is the motion of an object that is thrown or thrusted into the air such that the major force acting on an object is the force of gravity
(a) The parameters of the motion of the ball are;
Initial velocity of the ball = 7.8 m/s
Direction to which the ball is tossed = 24° below the horizontal
Time it takes the ball to strike the ground = 5.00 s
Location of the origin of the coordinates = The base of the building
[tex]h = v_{iy} \cdot t + 0.5 \cdot g \cdot t²[/tex]
Where;
h = The height of the window
[tex]u_{y}[/tex]
The initial vertical velocity = 7.8×sin(24°) ≈ 3.173 m/s
g = The acceleration due to gravity ≈ 9.81 m/s²
t = The time duration of the motion = 5.00 s
Therefore;
h = 3.173×5 + 0.5×9.81×5²≈ 138.49
The height of the window, h ≈ 138.49 meters
Given that the window shares the same x–coordinates with the base, which is 0, we have;
The coordinates of the window = (0, 138.49)(b) The x and y–component of the initial velocity are therefore;
v = 7.9 m/s × (cos(24°)•i - sin(24°)•j)
v = 7.22•i - 3.21•j
The x and y component of the velocity are therefore
x–component [tex] v_{ix} [/tex] = 7.22•i
y–component, [tex] v_{y} [/tex] = -3.21•j
Therefore;
The x–component is 7.22 m/s to the rightThe y–component is 3.21 m/s towards the ground(c) The equation of the x–component of the position is found as follows;
x = 7.9×cos(24°) × t = 7.22 •t
x = 7.22•ty = 7.9×sin(24°) × t+ 0.5× 9.81×t²
y = 3.21•t + 4.91•t²(d) The distance from the base of the building where the ball lands is given by the equation
d ≈ 3.21 × 5 ≈ 16.07
The ball lands 16.07 meters from the base of the building(e) The height from which the ball was thrown, h, is given by the y–coordinate in option (a) therefore;
h = 138.49 meters(f) When the distance traveled = 10 meters, we have;
[tex]h = v_{iy} \cdot t + 0.5 \cdot g \cdot t²[/tex]
Which gives;
10 = 3.21•t + 0.5×9.81×t²
Solving with a graphing calculator, gives;
t ≈ -1.79 or t = 1.14
The possible value for the time it takes to reach the point 10 meters is therefore;
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What is the measure of x?
HELP NEEDED ASAP
The value of x in the given right triangle is 8√5.
What is Pythagoras theorem?Pythagoras theorem states the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
The length of side z of the triangle is calculated as follows;
z² = y² + 4²
The length of side x is calculated as follows;
x² + z² = (16 + 4)²
x² + z² = 20²
substitute the value of z² into the equation,
x² + y² + 4² = 20²
x² + y² = 20² - 4²
x² + y² = 384
Considering the second triangle, with sides, 16, x and y, the value of side y is calculated as follows;
y² = x² - 16²
y² = x² - 256
x² + y² = 384
x² + x² - 256 = 384
2x² = 384 + 256
2x² = 640
x² = 640/2
x² = 320
x = √320
x = √(64 x 5)
x = √64 . √5
x = 8√5
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Discrete Math19. Rolling the Dice An experiment was conducted in whichtwo fair dice were thrown 100 times. The sum of the pipsshowing on the dice was then recorded. The following fre-quency histogram gives the resultsSum of Two Dice252015Frequency1032 3 4 5 6 7Value of Dice9 10 11 12(a) What was the most frequent outcome of the experi-ment?(b) What was the least frequent?(c) How many times did we observe a 7?(d) Determine the percentage of time a 7 was observed,(e) Describe the shape of the distribution
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
frequency histogram
Step 02:
discrete math:
sum of two dice:
we must analyze the graph to find the solution.
most frequent outcome:
value of dice = 8
frequency = 20
least frequent outcome:
value of dice = 2
frequency ≅ 2
how many times (7):
15 times (frequency)
percentage of times (7):
percentage (7) = (15 / 100) * 100%
percentage (7) = 15%
shape of distribution:
non-symmetric, bimodal
That is the full solution.
A. 3/5B.4/5C.3/4D.4/3
The tangent relation is given by the length of the opposite side to the angle over the length of the adjacent side to the angle.
So we have:
[tex]\begin{gathered} \tan (\beta)=\frac{AC}{BC} \\ \tan (\beta)=\frac{3}{4} \end{gathered}[/tex]Therefore the correct option is C.
Help me solve this please
Answer: a. 291/2020 b. 77/465 c. 874/2020 d.145/376 e. 41/157 f. 41/157 g. 53/157 h. 433/465 I. 335/376
Step-by-step explanation:
A. 291- column of loyal customers for 10-14 years over total amount. Question about the overall group 2020.
B. 77- people in the east that have been loyal 10-14 years in the east over the east group that's given that they're apart of 465.
C. 874 - customers loyal for more than 10 years in the west over the total amount. Question about the overall group 2020.
D.145 (45+100) - customers loyal for over 10 years in the west over the west group 376.
E. 41 people that have been loyal less than 1 year in the west over the group that has been loyal for less than 1 year 157.
F. 53 people that have been loyal less than 1 year in the south over the group that has been loyal for less than 1 year 157.
G.433 (465-32) people that have been loyal more than a year in the east over the east group 465.
I.335 (376-41) people that have been loyal in the west over the west group 376.
the area of rectangular pool
Answer:
multiply length times width.
Step-by-step explanation:
bacteria reveals a sample mean of ¯x = 70 hours with a standard deviation of s = 4.8 hours.What sample size should you gather to achieve a 0.4 hour margin of error? Round your answer up to the nearest whole number.
Solution
The formula for calculating margin of error is given to be
[tex]\begin{gathered} E=0.4 \\ n=? \\ \sigma=4.8 \\ p(x<\frac{Z_{\alpha}}{2})=\frac{1-0.9}{2}=\frac{0.1}{2}=0.05 \\ From\text{ the z-score and probability converter table, } \\ \frac{Z_{\alpha}}{2}=1.645 \end{gathered}[/tex][tex]\begin{gathered} Thus, \\ 0.4=1.645(\frac{4.8}{\sqrt{n}}) \\ Divide\text{ both sides by 1.645} \\ \frac{0.4}{1.645}=\frac{4.8}{\sqrt{n}} \\ 0.24316=\frac{4.8}{\sqrt{n}} \\ 0.24316\sqrt{n}=4.8 \\ \sqrt{n}=\frac{4.8}{0.24316} \\ \sqrt{n}=19.74 \\ n=19.74^2 \\ n=389.67 \\ n=390(nearest\text{ whole number\rparen} \end{gathered}[/tex]n = 390 bacteria (nearest whole number)
1. Joel purchased a picture frame. Each side measures 1 1/4 feet. a. What is the area of the frame?
Area = l x w
[tex]=1\frac{1}{4}\times1\frac{1}{4}[/tex]
convert to improper fraction and evaluate
[tex]=\frac{5}{4}\times\frac{5}{4}[/tex][tex]=\frac{25}{16}[/tex][tex]=1\frac{9}{16}ft^2[/tex]In a far away galaxy are two planets named Eenie and Meenie. Planet Eenie has
population of approximately 72,980,001, and Planet Meenie has a population o
approximately 54,908. About how many times greater is the population of Plan
Eenie than the population of Planet Meenie?
► 0:00/0:50
1.4 x 103
7.14 x 10-4
1.4 x 104
7 11 v 103
-
⠀
Population of Planet Eenie is 1.4 × [tex]10^{3}[/tex] times greater than the population of Planet Meenie.
Two planets named Eenie and Meenie.
Population of Planet Eenie = 72,980,001
Population of Planet Meenie = 54,908
We need to find how many times greater is the population of Planet
Eenie than the population of Planet Meenie. So, we need to follow the steps written below:
( Population of Planet Eenie / Population of Planet Meenie )
= ( 72,980,001 / 54,908 )
= 1329.1323
= 1.33 × [tex]10^{3}[/tex]
This calculated value is near option 2 i.e., 1.4 × [tex]10^{3}[/tex]. So, 1.4 × [tex]10^{3}[/tex] is the correct option.
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Identify the transformations for the function below. Check all that applyf(x) = -x2 - 4DilationHorizontal ShiftVertical ShiftReflection
Parent function:
[tex]f(x)=x^2[/tex]Transformations:
[tex]f(x)=a(x-h)^2+k[/tex]a indicates a reflection acrross x-axis (if it is a<0) and/or a stretch or shrink
h indicates a horizontal translation
k indicates a vertical translation
As you have:
[tex]undefined[/tex]explain why this is an error. What should she have done?
Answer:
3y = 80v - x
Step-by-step explanation:
she need to change the operation. x should be –
P (A) =0.17, P (A and B) =0.06, FIND P (B)
Answer:
P(B) = 0,35
Step-by-step explanation:
P(B) = P(A and B) divided by P(A)
The amount of air in a Suba diving tank with a capacity of 2400 liters is decreasing at a rate of 48
For given details the function is f(t) = 2400 - 48t
a) the amount of air in the tank is a function of the number of minutes it contain the air.
b) Domain of the function: [0, 50] and the domain is continuous one.
c) Graph of the function is attached below.
Function:
The function also know as expression, rule, or law that defines a relationship between one variable and another variable.
Given,
The amount of air in a scuba diving tank with a capacity of 2400 liters is decreasing at a constant rate of 48 liters per minute.
Here we need to find the following:
a) Whether the amount of air in the tank a function of the number of minutes?
b) Domain of the function
c) Graph of the function
Through the given question we know that,
The total amount of air in the tank = 2400 liters
Discharge unit per minute = 48 liters
Let us consider f(t) be the amount of air in a scuba diving tank.
where t represents the time in minutes.
Through the given information we get a function,
f(t) = 2400 - 48t
While using the given function, we can observe that the amount of air in the tank a function of the number of minutes.
Now, we need to find the domain of the function f(t)
Let us consider f(t) = 0
2400 - 48t = 0
2400 = 48t
t = 2400 / 48
t = 50
Therefore, t takes values in from the interval [0, 50]
We know that time is continuous to the function.
so, the domain is also continuous.
Now we have to plot the graph of the function..
Therefore, for given situation the function is f(t) = 2400 - 48t is attached below.
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If a ball is thrown upward at 64 feet per second from a height
of 4 feet, the height of the ball can be modeled by
S = 4 +64t - 16t² feet, where t is the number of seconds
after the ball is thrown. How long after the ball is thrown is the
height 32 feet?
[tex]S=4+64t-16t^2\implies \stackrel{\textit{at a height of 32}}{32=4+64t-16t^2}\implies 16t^2-64t-4+32=0 \\\\\\ 16t^2-64t+28=0\implies 4(4t^2-16t+7)=0\implies 4t^2-16t+7=0 \\\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{4}t^2\stackrel{\stackrel{b}{\downarrow }}{-16}t\stackrel{\stackrel{c}{\downarrow }}{+7}=0 \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]
[tex]t= \cfrac{ - (-16) \pm \sqrt { (-16)^2 -4(4)(7)}}{2(4)} \implies t = \cfrac{ 16 \pm \sqrt { 256 -112}}{ 8 } \\\\\\ t= \cfrac{ 16 \pm \sqrt { 144 }}{ 8 }\implies t=\cfrac{16\pm 12}{8}\implies t= \begin{cases} \frac{1}{2}&\textit{on the way up}\\\\ \frac{7}{2}&\textit{on the way down} \end{cases}[/tex]
In evaluating the expression 8+ 9/4 (-2) jenny found the volume to be 25/2. She thinks that the number is too great, but is not sure what she did wrong. Evaluate the expression
After evaluting the expression 8+ 9/4 (-2) we get 8 1/4.and result in decimals: 8.25
Given expression -
8+ 9/4 (-2) = ?
Combine the whole numbers and fractions together:
(8 – 2) + (9/4 - 0)
The whole numbers part is:
8 – 2 = 6
For the fractions part:
(9/4 - 0)
The Least Common Multiple (LCM) of 4 and 1 is 4. Multiply the numerator and denominator of each fraction by whatever value will result in the denominator of each fraction being equal to the LCM:
9/4 - 0 = 9/4 - 0/4
Now that the fractions have like denominators, subtract the numerators:
9 - 0/4 = 9/4
9 ÷ 4 = 2R1, therefore
9/4 = 2 1/4
Put the whole number and fraction together:
6 +2(1/4) 1
8 1/4.
Hence , the result of the expression 8+ 9/4 (-2) = 8 1/4.
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Cos(x)=-11/28, sin(x/2)
By using a trigonometric identity, we will see that the value of sin(x/2) is:sin(x/2) = ±√39/√56 = ± 0.834
How to find the value of sin(x/2)?Here we need to use the identity: (sin(x/2))^2 = (1 - cos(x))/2
So, we know that:
cos(x) = -11/28
Then:
(1 - cos(x)) = 1 + 11/28 = 28/28 + 11/28 = 39/28
Replacing the identity that we get:
(sin(x/2))^2 = (1 - cos(x))/2 ]= (39/28)/2 = (39/56)
Now we can apply the square root in both sides, so we will get:
sin(x/2) = ±√(39/56)= ±√39/√56 = ± 0.834
So, the value of sin(x/2) can be either 0.834 or -0.834.
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consider the circle centered at the origin and passing through the point (-2,0). (a) Give the equation of the circle.
As the circle is centered in the origin , we only need to know the radius of the circle. The radius is the distance from (0,0) to (-2,0) and it is 2. So the equation is
[tex]x^2+y^2=2^2[/tex]A weather researcher compared average monthly temperature data for Rio deJaneiro, Brazil, and Caracas, Venezuela.Rio de Janelro CaracasMean 76.5°F74.5°FRange 11.1°F17.4°FBased on these data, which statements are true?A. On average, Rio de Janeiro has a higher monthly temperature.However, temperatures in Caracas vary more.B. On average, Rio de Janeiro has a higher monthly temperature. Itsmonthly temperatures also vary more.C. On average, Caracas has a higher monthly temperature. However,temperatures in Rio de Janeiro vary more.D. On average, Caracas has a higher monthly temperature. Itsmonthly temperatures also vary more.
The mean and the average values are the same. They represent a dataset by calculating the central value.
The range can be understood as the variation of the data. The higher the range, the wider the variation.
From the table, we can see the average temperature of Rio de Janeiro is higher than in Caracas.
We can also see the variation of the temperature is higher in Caracas than in Rio de Janerio.
This corresponds to choice A.