Answer:
4,600,000,000
Step-by-step explanation:
Don't forget the order of operations
3.243 × 10⁸/7.05
= 46,000,000 × 10²
= 4,600,000,000
or 4.6 × 10⁹
Answer:
4.6x10 to the power of 5
Step-by-step explanation:
7.05×10
2
3.243×10
8
Divide them.
\frac{3.243}{7.05}\times \frac{10^8}{10^2}
7.05
3.243
×
10
2
10
8
Divide numbers and 10's separeately.
0.46\times 10^6
0.46×10
6
Subtract exponents.
(4.6\times 10^{-1})\times 10^6
(4.6×10
−1
)×10
6
Rewrite as a number bigger than 1
4.6\times (10^{-1}\times 10^6)
4.6×(10 −1 ×10 6 )
Associate
4.6\times 10^5
4.6×10 5
Add exponents
Daquin finished 30% of his homework in 27 minutes. How many minutes will it take him to finish the rest of his homework?.
In 27 minutes, Daquin completed 30% of his schoolwork. He must therefore finish another 70% of her homework.
We must multiply both sides of the equation by 3 to see how long it takes Daquin to finish 10% of the homework. It takes her 9 minutes.
We simply need to multiply our time estimate by seven to determine how long it will take her to complete the remaining 70% of her homework.
9 minutes are required for 10% of the homework.
63 minutes are required to complete 70% of the homework.
% finished equals 30%
Duration: 27 minutes
70% of the homework is still to be done.
Time required for the remaining task is 70/30 divided by 27 is equal to 63 minutes.
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The length and width of a rectangle that maximises the enclosed area are 162.5 yards. The maximum area is 26,406.25 square yards.
In the given question we have to find the maximum area of the rectangular area.
A farmer with 650 meters of fencing wants to enclose a rectangle plot that border on a river.
As we know that the perimeter of rectangle
P= 2(l+b)
Let length of the rectangle is x yards and width is y yards.
So the equation should be
2(x+y) = 650
Divide by 2 on both side we get
x+y = 325................(1)
From the area of rectangle is
A = xy
From the equation the value of y is 325-x.
Now putting the value of y
A = x(325-x)
A = 325x-x^2
On differentiating
dA/dx = 325-2x
Putting dA/dx=0
325-2x=0
Subtract 325 on both side we get
-2x= -325
Divide by -2 on both side we get
x = 162.5 yards
Now putting the value of x in the y=325-x
y=325-162.5
y=162.5 yards
So the maximum area is
A= 162.5*162.5
A= 26,406.25 square yards
Hence, the length and width of a rectangle that maximises the enclosed area are 162.5 yards. 26,406.25 square yards is the maximum area.
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For every 8 candles that you sell, you raise $96. You raise $288.
How many candles did you sell?
Answer:
24
Step-by-step explanation:
Start by finding the unit price. Unit price is the term for finding the price of one unit of an item, often used in word problems. We find this by dividing the cost of an item after a certain amount is sold, by that amount.
[tex]96/8 = \$12[/tex]
Now, we know the unit price is 12. Divide the end value of everything you sold by the unit price, 12.
[tex]288/12 = 24[/tex]
Therefore, you sold 24 candles.
Hope this helps!
The graph shows how many bottles a machine caps in a certain number of seconds.
(shown in the picture below)
Part A
What is the constant of proportionality, and what does it mean in this situation?
Use the drop-down menus to show and explain your answer.
The constant of proportionality is __ (Choices: 15, 30, 20) ; the machine caps __ (Choices: 30, 20, 15) bottles in ____________ (Choices: 1 second, 1 minute, 15 seconds)
Part B
Which of the following is an ordered pair on the graph? What does it represent in this situation?
A. ) (45, 90); the machine caps 45 bottles in 90 seconds.
B. ) (45, 900); the machine caps 45 bottles in 900 seconds.
C. ) (45, 900); the machine caps 900 bottles in 45 seconds.
D. ) (900, 45); the machine caps 900 bottles in 45 seconds.
Considering the proportional relationship graphed, it is found that:
A. The constant is of 20.
B. A pair on the graph is given as follows: C. ) (45, 900); the machine caps 900 bottles in 45 seconds.
What is a proportional relationship?A proportional relationship is a linear function with intercept zero in which the output variable y is given by the multiplication of the input variable x and the constant k, as follows:
y = kx.
Considering point (15, 300) on the graph presented, the constant is calculated as follows:
300 = 15k
15k = 300
k = 300/15
k = 20.
The input and the output are given as follows:
Input: number of seconds.Output: number of bottles capped.Hence option C is the correct option for item 2.
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Does this scatter plot show a linear association explain yes or no
No, The scatter plot does not show a linear association
What is graph?A graph is way of presenting data used by several disciplines.
There are many types of graphs and scatter plot is one of them.
scatter plot can be defined as set of dots plotted on a horizontal and vertical axis.
scatter plots can demonstrate the degree of connection, if any, between the values of observed quantities or events, they are crucial in statistics
The scatter plot does not show a straight line graph or a linear function. tracing the line shows a inverted shape of "s" which is not associated with linear functions.
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What is an equation of the line that passes through the points (6,2) and (7,1)?
The equation of the line that passes through the points (6,2) and (7,1) is y = -x+8
The points are
(6,2) and (7,1)
The slope of the line is the change in y coordinate with respect to the change in x coordinate of the function.
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the value in the equation
The slope of the line = (1-2) / (7-6)
= -1/1
=-1
The point slope form is
[tex](y-y_1)=m(x-x_1)[/tex]
Choose one point and substitute the values in the equation
y-2 = -1(x-6)
y-2 = -x+6
Move the 2 to right hand side of the equation
y = -x+6+2
y = -x+8
Hence, the equation of the line that passes through the points (6,2) and (7,1) is y = -x+8
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Forty students in the second grade class listed their hair and eye colors in the table below:
Brown hair Blonde hair Total
Blue Eyes 5 12 17
Brown Eyes 16 7 23
21 19 40
Are the events “blonde hair” and “brown eyes” independent?
The events “blonde hair” and “brown eyes” are not independent.
What are independent events?
The term "independent events" refers to those whose occurrence is not reliant on another event.
When two events A and B are independent then the intersection of the two events is equal to zero. i.e. They do not have any element in common.
But from the given table we can see that the intersection of the events of "blonde hair" and "brown eyes" exists.
Therefore, the events "blonde hair" and "brown eyes" are not independent.
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If x²+kx+16/9 is a perfect square. Find the value of k
Answer:
For x² + kx + 16/9 to be a perfect square, k should be equal to 8/3
Step-by-step explanation:
If x² + kx + 16/9 is a perfect square then it must satisfy the formula of (a + b)² i.e. equal to a² + 2ab + b².
So, first we will form a equal that looks similar to the formula:
[tex] \rm \implies {x}^{2} + kx + \dfrac{4 \times 4}{3 \times 3} \\ \\ \rm \implies {x}^{2} + kx + { \bigg( \dfrac{4}{3} } \bigg)^{2} [/tex]
Now by comparing we get,
[tex] \rm \implies k \cancel{x} = 2 \times \cancel{x}\times \frac{4}{3} \\ \\ \rm \implies k = \dfrac{8}{3} [/tex]
ADDITION AND SUBTRACT OF RATIONAL ALGEBRAIC EXPRESSION WITH UNLIKE DENOMINATORS. (See the picture)
The evaluation of the rational algebraic expression are presented as follows;
1. [tex]\dfrac{1}{3} +\dfrac{2}{5} = \dfrac{11}{15}[/tex]
2. [tex]\dfrac{x + y}{x} + \dfrac{x + y}{y} = \dfrac{x^2 + 2\cdot x \cdot y + y^2}{x \cdot y}[/tex]
3. [tex]\dfrac{3 \cdot x + 1}{x^2+2\cdot x +1} +\dfrac{5}{2\cdot x + 8} =\dfrac{11\cdot x^2 +36\cdot x +13}{2\cdot x^3 + 12\cdot x^2 + 18\cdot x+ 8}[/tex]
What is a rational algebraic expression?
A rational algebraic expression is an algebraic expression that consists of a quotient and divisor that consists of variables and numbers.
1. [tex]\dfrac{1}{3} + \dfrac{2}{5}[/tex]
[tex]\dfrac{1}{3} + \dfrac{2}{5} = \dfrac{5\times 1 + 2 \times 3}{3\times 5} =\dfrac{5 + 6}{15}[/tex]
[tex]\dfrac{5 + 6}{15} = \dfrac{11}{15}[/tex]
Therefore, we get;
[tex]\dfrac{1}{3} +\dfrac{2}{5} = \dfrac{11}{15}[/tex]
2. [tex]\dfrac{x + y}{x} + \dfrac{x + y}{y}[/tex]
[tex]\dfrac{x + y}{x} + \dfrac{x + y}{y} = \dfrac{y\times (x + y) + x\times (x+ y)}{x\cdot y}[/tex]
[tex]\dfrac{y\times (x + y) + x\times (x+ y)}{x\cdot y}= \dfrac{x^2+ 2\cdot y \cdot x +y^2 }{x \cdot y}[/tex]
Therefore;
[tex]\dfrac{x + y}{x} + \dfrac{x + y}{y} = \dfrac{x^2+ 2\cdot y \cdot x +y^2 }{x \cdot y}[/tex]
3. [tex]\dfrac{3 \cdot x + 1}{x^2 + 2\cdot x + 1} + \dfrac{5}{2 \cdot x + 8}[/tex]
[tex]\dfrac{3 \cdot x + 1}{x^2 + 2\cdot x + 1} + \dfrac{5}{2 \cdot x + 8} = \dfrac{(3 \cdot x + 1) \times (2\cdot x + 8) + 5 \times (x^2 + 2\cdot x + 1) }{(x^2 + 2\cdot x + 1) \times (2\cdot x + 8)}[/tex]
[tex]\dfrac{(3 \cdot x + 1) \times (2\cdot x + 8) + 5 \times (x^2 + 2\cdot x + 1) }{(x^2 + 2\cdot x + 1) \times (2\cdot x + 8)} = \dfrac{11\cdot x^2+ 36\cdot x+ 13}{2\cdot x^3 + 12\cdot x^2+18\cdot x+ 8}[/tex]
[tex]\dfrac{3 \cdot x + 1}{x^2 + 2\cdot x + 1} + \dfrac{5}{2 \cdot x + 8}=\dfrac{11\cdot x^2+ 36\cdot x+ 13}{2\cdot x^3 + 12\cdot x^2+18\cdot x+ 8}[/tex]
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Sherry has 15,200 dollars to invest in mutual funds and in bonds. Sherry has selected a mutual fund that earns 1% a year and a bond that earns 4% a year. If she wants to earn 548 at the end of the first year, how much does she need to invest in each type of account?
PLEASE ANSWER ILL DO ANYTHING. Like give brainliest mark, etc.
Sherry needs to invest 2000$ in mutual fund and 13200$ in bond to earn 548$ at the end of the year.
What is percentage?A percentage is just one of the many ways that a number, ratio, or fraction can be expressed. It is a number or ratio expressed as a fraction of 100.
Given:
Sherry has 15200$ to invest in mutual funds and in bonds.
Sherry has selected a mutual fund that earns 1% a year and a bond that earns 4% a year.
Here we need to find how much does she need to invest in each type of account if she wants to earn 548 at the end of the first year.
Here we have total amount = 15200$
So, let us consider x be the amount invested in mutual funds, then the amount invested in bonds will be 15200 - x.
It can be written in the following matrix
[x 15200-x ]
We know that the total amount earned at the end of the year is 548.
So, it can be written as
amount invested x percentage = final amount
[tex]\left[\begin{array}{cc}x&15200-x\\\\\end{array}\right][/tex]*[tex]\left[\begin{array}{ccc}1/100\\4/100\\\end{array}\right][/tex] = 548
We can simply it as
[x*1/100 + (15200 - x)*4/100] = 548
⇒ x/100 + 60800/100 - 4x/100 = 548
⇒ x + 60800 - 4x = 54800
⇒ -3x = 54800 - 60800
⇒ -3x = -6000
⇒ x = 2000
⇒ 15200 - 2000 = 13200
Therefore, Sherry invests 2000$ in mutual funds and 13200$ in bond to earn 548 at the end of the year.
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valuerelative frequency 10.15 20.30 30.45 40.10 if there are a total of 40 data values, with what frequency does the data value 1 occur?
The frequency of data value 1 that is 10 will be 6 as "Dividing each frequency by the total number of data values gives the relative frequency. So multiplying the relative frequency by the total number of data values gives the frequency."
What is relative frequency?The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event. The relative frequency is calculated by dividing each frequency by the total number of data values. Therefore, the frequency is calculated by multiplying the relative frequency by the total number of data values.
Here,
Value Relative frequency
10 0.15
20 0.30
30 0.45
40 0.10
data 1 value=10
Dividing each frequency by the total number of data values gives the relative frequency.
So, multiplying the relative frequency by the total number of data values gives the frequency.
40*0.15=6
Since "multiplying the relative frequency by the total number of data values gives the frequency," the frequency of the data value 1 that is 10 will be 6.
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2 1/2 divided by 2 1/4
Answer:
Step-by-step explanation:
(2 1/2) : (1/4) = 10/1 =10
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Dimensions of the area enclosed is 800 * 800 and the maximum area = 6,40,000 square yards.
Given:
Liana has 3200 yards of fencing to enclose a rectangular area.
Let l and b be the length and width.
we know that:
perimeter of rectangle = 2(l+b)
2l + 2b = 3200
l+b = 1600
b = 1600 - l
Area of rectangle A = lb
= l*1600-l
= 1600 l - l^2
Apply derivative:
dA/dl = 1600 - 2l
1600 - 2l = 0
1600 = 2l
l = 1600/2
l = 800
l+b = 1600
b = 1600 - 800
= 800
Area = 800*800
= 6,40,000
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Help me find one possible solution to the inequality and show how it makes sense in the situation.
A yearbook company promises to give the junior class a picnic if they spend at least $28,000 on yearbooks and class rings. Each yearbook costs $35, and each class ring costs $140. How many yearbooks and class rings must the junior class buy to get their picnic?
here is the inequality: 35x + 140y ≥ 2800
Answer:A - 200
B - 1 Class Ring and 796 yearbooks
C - No, they would come up short 2800 dollars
Step-by-step explanation:
What is the value of -2|6x - y| when x = -3 and y = 4?
O-44
O-28
O 28
O 44
Answer:
-44
Step-by-step explanation:
-2|6 * -3 - 4|
-2|-18-4|
-2|-22|
-2 * 22
-44
Juliana makes a prism 4 inches across and 4 inches wide but only 1 inch tall. She then decides to create
layers equal to her first one. Fill in the chart below, and explain how you know the volume of each new
prism.
Number of
Layers
3
5
7
Volume
Explanation
The volume of prism with 1 layer=16 inch³; The volume of prism with 3 layer=48 inch³;The volume of prism with 5 layer=80 inch³;The volume of prism with 7 layer=112 inch³.
What is volume?The total amount of space an object occupies in three dimensions is indicated by its volume. The term "capacity" describes something's ability to hold, absorb, or receive by an object .
Here,
Since each layer is of 1 inch.
So the volume of first prism,
=4*4*1
=16 inch³
When there is 3 layer, so the height is 3 inch,
=4*4*3
=48 inch³
When there is 5 layer, so the height is 5 inch,
=4*4*5
=80 inch³
When there is 7 layer, so the height is 7 inch,
=4*4*7
=112 inch³
The volume of a prism with one layer is equal to 16 inch³; with three layers, it is 48 inch³; with five layers, it is 80 inch³; and with seven layers, it is 112 inch³.
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What is the degree of the following
polynomial:
3x^5 + 4x^3 + 8x^2 - 14x +9
Answer:
Step-by-step explanation:
Here is an example:
Use this step by step explanation in your equation to help you find the answer.
For polynomial 2x2 - 3x5 + 5x6.
We observe that the above polynomial has three terms. Here the first term is 2x2, the second term is -3x5 and the third term is 5x6.
Now we will determine the exponent of each term.
(i) the exponent of the first term 2x2 = 2
(ii) the exponent of the second term 3x5 = 5
(iii) the exponent of the third term 5x6 = 6
Since, the greatest exponent is 6, the degree of 2x2 - 3x5 + 5x6 is also 6.
Therefore, the degree of the polynomial 2x2 - 3x5 + 5x6 = 6.
which is a perfect square 20 13 25 24 14 10 7 11 8
HELPPPP PLSPLSPPSPPPLSPSLPLLSLPSLP
Answer: What do those numbers mean
Step-by-step explanation:
Pls help/ A function (x) is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
Enter your answer in the box.
f(x)=
The function rule in slope-intercept form is y = -4x - 2
How to calculate the slope-intercept form of this function?Mathematically, the slope-intercept form of a straight line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the intercept.From the graph of this line, we have the following data points:
Point (x, y) = (-1, 2)
Point (x, y) = (0, -2)
In Mathematics, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (-2 - 2)/(1 - 0)
Slope, m = -4/-1
Slope, m = -4
Note: The y-intercept occurs at the point where the x-value is equal to zero (0).
Now, we can write the function rule for this line in slope-intercept form as follows:
y = mx + c
y = -4x - 2
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PLEASE HELP!
6) You are playing a game with your friend that involves dice and 10 cards numbered 1-10.
a) If you were to roll the dice and pick a random card, what is the probability of rolling a 4 and picking a 4 from the numbered deck of cards?
b) If you draw 3 cards from the deck of numbered cards (without replacement) what is the probability of drawing 3 even cards?
c) If you roll a die 3 times, what is the probability of rolling 3 even numbers?
d) At one point you start rolling the die and recording your results. You suddenly realized that for the last 30 rolls of the die you have rolled an even number! What is the probability that your 31st roll is also an even number?
Answer:
1-10.
Step-by-step explanation:
you're planning on making 5 meatloafs for a party. you go to the store to buy breadcrumbs, and see they are sold by the canister. how many canisters do you need to buy?
Without decimal, 4 canisters need to buy for making 5 meatloafs for party or if answer in decimal values needed then it is 3.333 canisters.
From the provided data, we have
number of meatloafs = 5
Here we have need the cup measurements the number of meatloafs made per recipe and the net weight of canister.
net weight of the contents of 1 canister = 15 ounces
1 cup = 8 ounces
1.25 cups = 10 ounces
10 ounces of breadcrumbs makes 1 meatoafs.
but we made 5 meatloafs so, for 5 meatloaf needed breadcrumbs = 5×10
= 50
If we consider 4 canisters then
15ounces × 4 canisters = 60 ounces which are 10 more than the needed ( > 50 ounces.
and if we are consider 3 canisters then
15 ounces × 3 canisters = 45 ounces which is not enough.
So, we need 4 canisters of breadcrumbs and we will have 2/3 of a canister left over.
approximately 3.333 is a value of needed canisters in decimals values. If decimal values are not need ,i.e, whole are canisters are not partial then 4 canisters is right .
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Complete question:
you're planning on making 5 meatloafs for a party. you go to the store to buy breadcrumbs, and see they are sold by the canister. how many canisters do you need to buy?
First, determine what information you need to answer this question, then click here to display that info (along with other info).
How much breadcrumbs does the recipe call for? It calls for 1 1/4 cups of breadcrumbs. How many meatloafs does the recipe make? It makes 1 meatloaf.
How many servings does that recipe make? It says it serves 10.
How big is the canister? It is cylindrical, 3.5 inches across and 7 inches tall.
What is the net weight of the contents of 1 canister? 15 ounces.
How much does a canister cost? $2.39
How much does a cup of breadcrumbs weigh? I'm not sure, but maybe something from the nutritional label will help.
What is 27/31 in its simplest form
Answer:
27/31
Step-by-step explanation:
Use the diagram. What is measure angle 2 + measure angle 3?
Enter the correct value in the box.
measure angle 2 + measure angle 3 = ?
Answer:
The red symbol drawn over ∠2 and ∠3 indicates that the two angles total 90°. Therefore:
[tex]m\angle{2}+m\angle{3}=90^{\circ}[/tex]
The linear equation y = negative 2 x + 4 is represented on the graph below.
On a coordinate plane, a line goes through (0, 4) and (2, 0).
A second linear equation is represented by the data in the table.
x
y
–4
–3
0
–1
2
0
6
2
What is the solution to the system of equations?
(2, 0)
(0, 4)
(0, –1)
(4, –4)
The solution to the system of equations will be;
⇒ (2, 0)
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The first equation is,
y = - 2x + 4
And, A line goes through (0, 4) and (2, 0).
Now,
For the second linear equation;
The coordinates are,
(-4, -3) (0, -1) , (2, 0) , (6, 2)
Hence, The equation of line passes through the points (-4, -3) and (0, -1).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 1 - (-3)) / (0 - (-4))
m = 2 / 4
m = 1/2
Thus, The equation of line with slope 1/2 is,
⇒ y - (-3)= 1/2 (x - (-4))
⇒ y + 3 = 1/2 (x + 4)
⇒ y = 1/2x + 2 - 3
⇒ y = 1/2x - 1
Now, We find the value of system of equations;
y = - 2x + 4
y = 1/2x - 1
Solve both above equation, we get;
1/2x - 1 = - 2x + 4
1/2x + 2x = 4 + 1
5/2x = 5
x = 2
And, y = 1/2 (2) - 1 = 0
Thus, The solution to the system of equations will be;
⇒ (2, 0)
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Answer:
A
Step-by-step explanation:
if g(x) = x^2 - 4x find the value for g(2n)
Answer: [tex]g(2n)=4n^2 -8n[/tex]
Step-by-step explanation:
Substituting [tex]2n[/tex] for [tex]x[/tex],
[tex]g(2n)=(2n)^2 -4(2n)\\\\g(2n)=4n^2 -8n[/tex]
What is the slope of the line that contains points (2, 9) and (8, 7)?
Answer:
-1/3
Step-by-step explanation:
m = y2-y1/x2-x1 formula for slope
m = 7-9/8-2 Plug in the numbers
m = -2/6 Subtract 7-9 and 8-2
m = -1/3 Simplify
Ben watched 3/8 of his television show. There are still 40 minutes left. How long does the whole program last?
The show is 1 hour 4 minutes long.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Ben watched 3/8 of his television show.
There are still 40 minutes left.
let the show be x long.
So, 3/8x + 40 = x
x- 3/8x= 40
5x/8 = 40
x= 320/5
x= 64 minutes
x= 1 hour 4 minutes
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a person must score in the upper 4% of the population on an iq test to qualify for membership in mensa, the international high iq society, if iq scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for mensa. (2 decimals)
A person must have a score of 126.26 to qualify Mensa.
it is given that,
Mean [tex](\mu) = 100,[/tex]
Standard deviation [tex](\sigma) = 15[/tex].
A person must score in the upper 4% of the population,
100% - 4% = 96% = 0.96
P(X < Xo) = 96% = 0.96
P(X < 1.7507) = 0.96 ....................................using the Normal distribution table,
Or, when the Invnorm function is used, Invnorm(0.96) = 1.7507
Therefore, The required value of X is,
[tex]Z = \frac{(X - \mu )}{ \sigma }[/tex]
1.7507 = (X - 100) / 15
X - 100 = 26.26
X = 100 + 26.26
X = 126.26
thus, the score a person must have to qualify Mensa is 126.26.
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3. Martin finishes a swim race in 78.934 seconds. His teammate, Abby finishes the race in 83.978 seconds and their last teammate finishes the race in 84.765 seconds.
If the teammates were to have a combined time of less than 250 seconds to qualify to the next round, did they qualify or not? How do you know?
help me please i really need help!
The function f(x) = x2 is graphed above. Which of the graphs below represents the function g(x) = x2 + 3 ?
Using a translation, the graph of the function f(x) = x² + 3 is given by the image at the end of the answer.
What is a translation?Among the many transformations that a function or a figure can undergo is a translation, and other examples are reflections, rotations and dilation.
The difference of a translation from these other transformations is that the only thing that changes for the function is the position. The inclination, orientation and length all remains constant.
The four possible types of a translation are given as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The parent function in this problem is given as follows:
f(x) = x².
Which has the U format of a parabola and a vertex at the origin (3,3).
The translated function is given as follows:
g(x) = x² + 3.
The addition by 3 means that the function was translated up 3 units, as shown in the image given at the end of the answer.
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