Answer:
D. sqt5
Step-by-step explanation:
The best process is to start eliminate answers. It can not be C because
-8 + 8 =0. 0 is not an irrational number. Sqt4 is 2, 2+8=10. 10 is a real rational number. 5/9 is not an irrational number because it is a ratio of 5 to the non-zero quotient of 9. Sqt5 is the only irrational number, and when added to 8, it is still irrational.
A circle has centre (0, 0) and it passes through the point (5, -3)
Find the radius of the circle, in surd form.
Answer:
radius = [tex]\sqrt{34}[/tex]
Step-by-step explanation:
The radius r is the distance from the centre to a point on the circle.
Use the distance formula to calculate r
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (5, - 3)
r = [tex]\sqrt{(5-0)^2+(- 3-0)^2}[/tex]
= [tex]\sqrt{5^2+(-3)^2}[/tex]
= [tex]\sqrt{25+9}[/tex]
= [tex]\sqrt{34}[/tex]
The daily low temperature in Guangzhou, China Varies over time in a periodic way that can be modeled by a trigonometric function. The period of change is exactly one year. the temperature peaks around July 26 at 78°F and has its minimum half a year later at 49°F. assuming a year is exactly 365 days July 26 is 206/365 of a year after January 1. Find the formula of the trigonometric function that models the daily low temperature T in Guangzhou t years after January 1, 2015 defined the function using radians
Answer:
T(t) = 14.5cos(2π(t -206/365)) +63.5
Step-by-step explanation:
The function can be written as ...
T = A·cos(2π(t -206/365)) +B
where A is half the difference of the high and low temperature values, and B is the average of the high and low temperature values.
A = (78-49)/2 = 29/2 = 14.5
B = (78 +49)/2 = 127/2 = 63.5
The value 206/365 is the horizontal right shift of the peak of the function. That makes the peak occur on July 26, as required.
Filling in these values gives us the function ...
T(t) = 14.5cos(2π(t -206/365)) +63.5
Determinado automovel, apos sua compra, perde 10% do valor ano a ano nos 3 preimeiros anos. Calcule o valor do automovel ao final desse periodo sabendo que ele foi comprado por R$80.000
Answer:
The value of the car after 3 years is R$58.320.
O valor do carro ao final desse período é R$58.320.
Step-by-step explanation:
The value of the car after t years is given by the following equation:
[tex]V(t) = V(0)(1-r)^{t}[/tex]
In which V(0) is the initial value and r is the yearly depreciation rate.
In this question, we have that:
[tex]V(0) = 80000, r = 0.1[/tex]
So
[tex]V(t) = V(0)(1-r)^{t}[/tex]
[tex]V(t) = 80000(1-0.1)^{t}[/tex]
[tex]V(t) = 80000(0.9)^{t}[/tex]
Value of the car at the end of 3 years:
[tex]V(3) = 80000(0.9)^{3} = 58320[/tex]
The value of the car after 3 years is R$58.320.
O valor do carro ao final desse período é R$58.320.
What is the volume of a cylinder in cubic feet with a height of 8 feet and a base diameter of 18 feet
Answer:
The volume of a cylinder:
[tex]V \approx 2035.75[/tex] [tex]ft^3[/tex]
Step-by-step explanation:
-To find the volume of a cylinder, you first need the formula:
[tex]V = \pi (\frac{d}{2})^2 h[/tex]
[tex]d =[/tex] diameter
[tex]h =[/tex] height
-Use the following diameter and height for the formula:
[tex]V = \pi (\frac{18}{2})^2 8[/tex]
-Then, you solve:
[tex]V = \pi (\frac{18}{2})^2 8[/tex]
[tex]V = \pi \times (\frac{18}{2})^2 \times 8[/tex]
[tex]V = \pi \times (9)^2 \times 8[/tex]
[tex]V = \pi \times 81 \times 8[/tex]
[tex]V = \pi \times 648[/tex]
[tex]V = 648\pi \approx 2035.752[/tex]
-Since the hundredth place is 2, It cannot be rounded to the nearest hundredths place, so it would be:
[tex]V \approx 2035.75[/tex] [tex]ft^3[/tex]
What is the coefficient in the following expression?
5a to the 2 power subtracted by 7
a)7
d)2
c)5
b)a
Answer:
c)5
Step-by-step explanation:
Coefficient is always the numerical value before the variable
I hope this helped and have a good rest of your day!
helppppppppppppppppp
Answer:
3/4 of an inch
Step-by-step explanation:
The longest plant is 7/8 of an inch
The shortest plant is 1/8 of an inch
7/8 - 1/8 = 6/8
Simplifying = 3/4
Which number has the least value?
Answer:
Your annswer is b
Step-by-step explanation: because it is least than all of the others
The number that has the least value is given as -13.142.
What are arithmetic operations?The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.
The number given in the options are |-10.869|, -14⁶/₇, 9.21 and |-10.25|.
Write all the numbers in one equivalent form as below,
⇒ |-10.869| = 10.869
⇒ -14⁶/₇ = -14 + 6/7 = -13.142
⇒ 9.21
⇒ |-10.25| = 10.25
It is clear from the equivalent form that the least value is -13.142.
Hence, the the least value number is obtained as -13.142.
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compound interest: if 1000$ is compounded continuously at 3% interest, how much money will you have in 5 years? (use the growth formula y=Ce exponent of kt)
Answer:
The money you will have in 5 years: 1000 x (1 + 3/100)^5 = 1159.27$
Hope this helps!
:)
A spinner has 5 equal sections numbered 1 to 5. What is the probability of the spinner stopping on a number that is a multiple of 2 or is less than 3?
help!!!!!!!!!plz.....
Answer: 1/5, .2, and or 20%
Step-by-step explanation:
The only multiple of 2 that is less than 3 and greater than 1 is 2, so there is a 1/5, .2 and or 20% chance of this happening
8. A teacher is cutting along the diagonal of a rectangular piece of construction
paper for a bulletin board which is 11 inches long and 8.5 inches wide. What
will be the length of the cut?
Answer:
The length of the diagonal is 13.90 inches
Step-by-step explanation:
This question can be remolded as calculating the length of the diagonal of a rectangle with dimensions 11 inches by 8.5 inches.
The diagonal refers to that length that runs from one inner edge of the rectangle to the other inner edge of the rectangle.
To calculate this length, we shall be making use of the Pythagoras’ theorem
Please check attachment for the kind of figure i’m trying to paint.
Let’s call the diagonal D
Using the Pythagoras’ theorem,
D^2 = 11^2 + 8.5^2
D^2 = 121 + 72.25
D^2 = 193.25
D = √193.25
D = 13.90 inches
Find the area of the shaded regions:
The pink is the shaded region
Answer: 5184.
Step-by-step explanation:
You do 72 x 72.
If nominal GDP is 2400 and the money supply is 400, what is the velocity?
Answer:
The velocity of money is 6.
Step-by-step explanation:
Nominal Gross Domestic Product is the Gross Domestic Product that has been determined by the current prices of goods and services in a market.
Money velocity expresses the rate at which money moves from one entity to another in a given economy. It it the ratio of the nominal Gross Domestic Product to the money supply in an economy.
i.e V = [tex]\frac{P * Y}{M}[/tex]
where: V is the velocity of money, P x Y is the nominal GDP i.e price level x output/real GDP, and M is the money supply. High velocity of money causes an increase in inflation.
Given that, nominal GDP = 2400 and money supply = 400, then;
V = [tex]\frac{2400}{400}[/tex]
= 6
Therefore the velocity of money is 6.
The length of a rectangle is 5 m less than twice the width, and the area of the rectangle is 52m ^ 2 . Find the dimensions of the rectangle.
The dimension of the rectangle is 8m by 6.5m respectively
Area of a rectangleThe formula for calculating the area of a rectangle is expressed as;
A =lw
If the length of a rectangle is 5 m less than twice the width, then;
l = 2w - 5
Substitute
A = w(2w-5)
52 = 2w² - 5w
2w² - 5w = 52
2w² - 5w - 52 = 0
(2w−13)(w+4)=0
Step 2: Set factors equal to 0.
2w−13=0 or w+4=0
w =13/2 or 6.5m
Determine the length
l = 2w - 5
l = 2(6.5) - 5
l = 13 - 5
l =8m
Hence the dimension of the rectangle is 8m by 6.5m respectively
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Tickets for a basketball game cost $20 for upper-level seats and $30 for lower-level seats. Tickets at the same venue
for an ice hockey game cost $15 for upper-level seats and $35 for lower-level seats. If tickets for all seats are sold,
the venue generates $7000 in revenue for a basketball game and $6500 for a hockey game. How many upper and
lower-level seats does the venue have?
Let x represent the number of upper-level seats.
Let y represent the number of lower-level seats.
20x + 30y = 7000
15x + 35y = 6500
The venue has
upper-level seats and lower-level seats.
Answer:
200 and 100
Step-by-step explanation:
Just did it:)
Answer:
The number of upper-level seats = 200
The number of lower-level seats = 100
Step-by-step explanation:
Given:
x = the number of upper-level seats.
y = the number of lower-level seats.
According to the question:
20x + 30y = 7000
15x + 35y = 6500
Multiply first equation by 3 and second by 4 then subtract them
[tex]3(20x + 30y) - 4(15x + 35y ) = 3(7000)-4(6500)\\60x+90y-60x-140y=-5000\\-50y=-5000\\y=100[/tex]
Plug y=100 in 20x + 30y = 7000.
[tex]20x + 30y = 7000\\20x + 30(100) = 7000\\20x+3000=7000\\20x=4000\\x=200[/tex]
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Ellie bought two pairs of shoes during a BOGO (Buy One, Get One) sale. She received a 20% discount on the second pair of shoes. The regular price of each pair of shoes was $49.99. How much did Ellie pay for the two pairs of shoes, excluding tax?
Answer:
89.98
Step-by-step explanation:
49.99 x 20% = 9.998
So, 20% of 49.99 is 10.
49.99 - 10 = 39.99 To get the Total of the discounted item.
49.99 + 39.99 = 89.98 Add final totals to get answer
Cleo sold lemonade at her lemonade stand. On Saturday, she sold 6 pitchers of lemonade. On Sunday, she sold as much lemonade as on Saturday. How many pitchers of lemonade did Cleo sell on Sunday?
Answer:
12 pitchers
Step-by-step explanation:
Saturday, 6 pitchers
Sunday, same number of pitchers with Saturday, = 6 pitchers
Total pitchers = 6 + 6 = 12 pitchers
Answer:
Cleo sold 6 pitchers of lemonade on Sunday.
Step-by-step explanation:
Cleo sold lemonade at her lemonade stand.
She sold 6 pitchers on Saturday.
On Sunday, she sold as many pitchers as Saturday.
This implies that she sold 6 pitchers too.
She sold 6 pitchers on Saturday, and 6 pitchers on Sunday.
Mr. Williams paid $1,250 in cash for a new television set. If he had bought it using the store's payment plan, he would have had to pay a deposit of $350 and 9 monthly installments of $150. How much money did he save by paying in cash?
Answer:
$450
Step-by-step explanation:
Mr. william's paid $1250 in cash for a new television set. But if he was to use the store's deposit plan, he will have to make some installmental payment after paying an initial deposit.
Initial deposit = $350
Installmental payments of $150 for 9months.
His total payment will be = Initial payment + the total amount of the installmental payment.
$350 + (9 x $150) = $350 + 1350 = $1700
$1700 - $1250 = $450 savings
By paying in cash he will be saving an amount of $450.
Twelve-year-olds have heights that are normally distributed with a mean of heights of 57 inches and a standard deviation of 4.6 inches. what percent of 12-year-old boys will have heights less than 55 inches?
A) 33%
B) 37%
C) 42%
D) 49%
Answer:
A
Step-by-step explanation:
To calculate this, the first thing we need to do is to calculate the z-score
Mathematically,
z-score =( x - mean )/SD
according to the question, X = 55 inches, mean = 57 inches and SD = 4.6 inches
we plug these values into the equation
z-score =( 55-57)/4.6 = -2/4.6 = -0.4348
The required probability we are trying to calculate is;
P( z < -0.4348) or simply P(x<55)
To calculate this probability we use the standard score table
From the standard score table,
P( z < -0.4348) = 0.33186
In percentage this is 33.186%
To the nearest percentage, this is 33%
Y=X-2
-X+Y=10
A)Parallel
B)neither
C)perpendicular
Answer:]]
The slope of these two linear equations is the same so the would be Parallel.
y = mX + B where m is the slope.
In this case the slope is 1 for both equations.
y = x -2
y = x + 10
They would be exactly 12 units apart too.
Step-by-step explanation:
Rewrite (2 + 6)5 using the Distributive Property.
Answer:
5 * 2 + 6 * 5
Step-by-step explanation:
Distributive Property.
A concrete planter is formed from a square-based pyramid that was inverted and placed inside a cube.
A. What is the slant height of the pyramid?
B. What is the surface area of the composite figure?
C. How many cubic yards of concrete are needed to make the planter?
Answer:
Notice that each edge of the cube is 2 yards long, and the height of the pyramid is 2 yards long too.
The slant height refers to the height of a triangle on its face, which forms a right triangle with the height of the pyramid and half side. Using Pythagorean's Theorem, we have
[tex]s^{2}=1^{2} +2^{2}\\ s=\sqrt{5}[/tex]
Therefore, the slant height is the square root of 5, in yards units. (A)
The surface of the composite figure is the sum of the surface area of both volumes.
[tex]S_{composite}=S_{cube} +S_{pyramid}\\ S_{composite}=5(2)^{2} +(2)^{2} +\frac{1}{2} (8)(\sqrt{5} )=20+4+4\sqrt{5} \\ S_{composite}\approx 32.9 yd^{2}[/tex]
Therefore, the surface of the composite figure is 32.9 square yards. (B)
The concrete needed will fill the empty space between the cube and the pyramid, so we have to find the difference between their volumes.
[tex]V_{concrete}=V_{cube} -V_{pyramid}=2^{3}-\frac{1}{3}(2)^{2} (2)=8-\frac{8}{3} \\V_{concrete} \approx 5.33 yd^{3}[/tex]
Therefore, we need 5.33 cubic yards of concrete to make the planter. (C)
Answer:
A. 2.24 yd
B. 53.67 yd²
C. 5.33 yd³
Step-by-step explanation:
Here we have;
Height of the pyramid = 2 yd
Side length of pyramid base = 2 yd
Therefore, the slant height forms a right triangle with the height of the pyramid and half the base hence;
(Slant height)² = (2·yd)² + (2·yd/2)² = 4·(yd)² + (yd)² = 5·(yd)²
∴ Slant height = √5 yards = 2.24 yd
B. The surface area of the cube with one side open is found as follows;
Surface area of container cube = 5 × (2·yd)² = 20 yards²
The surface area of the pyramid = Base area + 1/2 perimeter of base × Slant height
Since the base is open, we have;
The surface area of the pyramid = 1/2 perimeter of base × Slant height
= 1/2 × (4 × (2·yd))×yd·√5 = 4·yd×yd·√5 = 4·√5·(yd)²
Hence total surface area of the planter = Surface area of container cube + surface area of the pyramid
total surface area of the planter = 20·yd² + 4·√5 yd² = 24·√5 yards²
C. The volume of concrete needed to make the planter is the volume of the cube concrete container less the volume of the inverted pyramid
Volume of the cube = 2 × 2 × 2 = 8 yd³
Volume of the inverted pyramid = 1/3 × Base area × Height
Volume of the inverted pyramid = 1/3 × 2 × 2 × 2 = 8/3 yd³
Therefore, volume of the concrete needed = 8 yd³ - 8/3 yd³ = 16/3 yd³ = 5.33 yd³.
Which of the following probabilities is the greatest for a standard normal distribution?
P(-1.5 575-0.5)
P(-0.5 SZ30.5)
P(0.5 5731.5)
P(1.5 523 2.5)
Answer: it’s actually b for edge 2020
Step-by-step explanation:
The probabilities greatest for a standard normal distribution is
P(-0.5 SZ30.5) i.e. 38.2%
What is a standard normal Distribution ?A special normal distribution where the mean is 0 and the standard deviation is 1. It is also called the z-distribution .
For the data given in the question
P(-1.5 575-0.5)
P(-0.5 SZ30.5)
P(0.5 5731.5)
P(1.5 523 2.5)
[tex]P_{r} (-1.5 \leq z \leq 0.5) = 0.092 +0.15=0.242\\\\P_{r} (-0.5 \leq z \leq 0.5)= 0.191+0.191= 0.382\\\\P_{r} (0.5 \leq z \leq 1.5)= 0.15+0.092=0.242\\P_{r} (1.5 \leq z \leq 2.5)= 0.044+0.017=0.061[/tex]
From the given data the second data is the highest 0.382 , so the correct answer is P(-0.5 SZ30.5).
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The graph of a polynomial is shown below. Is its highest power even or odd? Explain.
Answer:
Step-by-step explanation:
the graph is at the highest power at the top left corner because the graph shape has a even or odd chance so that is the answer
It's highest power is odd
What is graph of polynomial ?
The graph of a polynomial function will touch the x-axis at zeros with even multiplicities. The graph will cross the x-axis at zeros with odd multiplicities. The sum of the multiplicities is the degree of the polynomial function.
According to the question,
Graph of polynomial is shown in given graph,
(1) at point A graph passes linearly
(2) At point b, graph passes x-axis cubically
(3) At point c, Graph passes x-axis linearly
Hence, polynomial having degree 5
Hence, it's highest power is odd
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Find the arc length of major arc GH. Round your answer to the nearest tenth.
Answer:
42.1 cm
Step-by-step explanation:
The length of the arc is circumference of the circle - length of minor arc GH
circumference of circle = 2 * π * r = 2 * π * 9.1 = 18.2 π cm
The length of the minor arc = angle/360 * 2 * π * r
Now this is tricky, the angle is 360-265 = 95
The length of the minor arc = 95/360 * 2 * π * 9.1 = 4.80 π
Length of major arc = 18.2 π -4.8 π = 13.4 * π = 13.4 * 22/7 = 42.11cm
Matthew invested $5,800 in an account paying an interest rate of 4.9% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 7 years?
Answer:
A≈8173.18
Step-by-step explanation:
The All-Clean Laundry Company washes towels for a nearby hotel. The function f(x) gives the number of loads required whenthere are x bins of towels to be washed. What does f(9) > 12 tell you?
Answer:
B. It takes more than 12 loads to wash 9 bins of towels.
Step-by-step explanation:
The function f(x) gives the number of loads
Where x= bins of towels
If f(9) > 12
Number of bins of towels =9; andNumber of Loads, f(x)>12Therefore, f(9) > 12 tells us that it takes more than 12 loads to wash 9 bins of towels.
The correct option is B.
There are 19 sweaters in a closet and some sweaters are in the dresser as well.If the total number of sweaters is 60,which of the following equations is correct?A.19 + s=60,B.19× s=60,C.19÷s=60,D.60÷s=19
Answer:
A
Step-by-step explanation:
The table below shows the relationship between the number of miles traveled and the number of gallons of gas used. Which of the following statements best represents the relationship
A. The nu,ber of miles is the dependent quantity and the number of gallons os the dependent quantity
B. The number of miles and the number of gallons are both dependent quantities.
C. The number of gallons and the of miles are both independent quantities.
D. The number of miles is the independent quantity and the number of gallons is the independent quantity.
plz help
Answer:
Number of miles = dependent variable
Number of gallons used = independent variable
Step-by-step explanation:
In order for the driver to see how many miles the car can run, they must first see how many gallons of gas they have in the car. The number of miles depend on the number of gallons used. So, your answer would be letter choice A.
The statement which best represents the relationship is that, the number of miles is the dependent quantity and the number of gallons is the independent quantity.
What are Dependent and Independent Variables?Dependent variable are variables which depends on another variable to take it's value.
Independent variables are those which does not depend on other variables.
Given is a table which represents the number of miles travelled and the number of gallons of gas used.
From the table, if x represents the number of gallons of gas used and y represents the number of miles travelled, then the equation can be written as,
y = 35x
It is clear that, the value of y depends on the value of x.
So, x is the independent variable and y is the dependent variable.
That is, number of gallons of gas used is the independent variable and number of miles travelled is the dependent variable.
Hence the number of miles is the dependent quantity and the number of gallons is the independent quantity.
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Factor completely.
4 - 12x + 9x^2
[tex]4-12x+9x^{2} \\4-6x-6x+9x^{2} \\2(2-3x)-3x(2-3x)\\(2-3x)(2-3x)\\(2-3x)^2[/tex]
Find the common difference of the arithmetic sequence 13,10,7
Answer:
-3 I think
Step-by-step explanation:
well 10-7=3 and 13-10=3
but since it is greater number first it would make it a -3
