Jessica's position relative to the surface of the water after making 4 additional stops is 45 meters below the surface.Option(A) is correct.
What is sea diving?Divers who engage in scuba diving use breathing apparatus that is entirely independent of a surface air source. Christian J. Lambert-sen came up with the moniker "scuba," which stands for "Self-Contained Underwater Breathing Apparatus," in a 1952 trademark application.
According to question:Jessica's position relative to the surface of the water can be represented by the following arithmetic sequence:
[tex]$$25, 30, 35, 40, 45$$[/tex]
where the first term is 25 and the common difference is 5 (the distance between each stop).
To find the fifth term (her position after making 4 additional stops), we can use the formula for the nth term of an arithmetic sequence:
[tex]$$a_n = a_1 + (n-1)d$$[/tex]
where [tex]$a_1$[/tex] is the first term, d is the common difference, and n is the term number.
Plugging in the values we know, we get:
[tex]$$a_5 = 25 + (5-1)5 = 45$$[/tex]
Therefore, Jessica's position relative to the surface of the water after making 4 additional stops is 45 meters below the surface.
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Winston is baking a pie. The diameter of the pie is 12 inches. What is the area of the pie? Use 3.14 for pi and round your answer to the nearest tenth.
The area of the pie is approximately 113.0 square inches.
What is the significance of pi in math?The ratio of a circle's circumference to its diameter is denoted by the mathematical constant pi . It is roughly equivalent to 3.14159 and is not repetitive or terminal. As pi is an irrational number, it cannot be written as an exact fraction of two integers and its decimal representation never ends. Pi is used to compute the characteristics of circles, spheres, cylinders, and other curved objects in many branches of mathematics and science, including geometry, trigonometry, calculus, physics, and engineering.
The area of the circle is given as:
A = πr²
Here, diameter = 12, thus radius is 6 inches.
Substituting the values:
area = 3.14 x (6)²
area = 113.04 square inches
Hence, the area of the pie is approximately 113.0 square inches.
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Would a line through these two points A and B be a good fit for the data? Why or why not?
(Please don’t mind the other words! TvT
miguel rode his bicycle 4 miles less than 5 times the number nathen rode. if Miguel rode his bicycle 6 miles, how many miles did nathan ride?
Answer:Hence, Nathan rode 2 miles
Step-by-step explanation:ask if you need any questions
Which of the series in exercises 17–56 converge, and which diverge? use any method, and give reasons for your answers
The given series diverges to negative infinity as the terms cancel out, leaving only two terms at the beginning and end of the series.
To determine the convergence of the given series, we can use the telescoping series method.
Let's write out a few terms of the series to see if we can spot a pattern:
n=1: 1/2 - 3/4 = -1/4
n=2: 2/3 - 4/5 = -2/15
n=3: 3/4 - 5/6 = -1/8
n=4: 4/5 - 6/7 = -2/35
...
We can see that the terms of the series cancel out, leaving only two terms at the beginning and end of the series. Therefore, we can write the series as:
∑ (n/n+1 - n+2/n+3) = 1/2 - (n+2)/(n+3)
As n approaches infinity, the second term approaches 1, so the series diverges to negative infinity.
Therefore, the given series diverges.
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_____The given question is incomplete, the complete question is given below:
Which of the series in exercises 17–56 converge, and which diverge? use any method, and give reasons for your answers
(∑ ∞ to n = 1) = (n/n+1 - n+2/n+3)
Any number that can be written as a decimal, write as a decimal to the tenths place.
Given A = (-3,2) and B = (7,-10), find the point that partitions segment AB in a 1:4 ratio.
The point that partitions segment AB in a 1:4 ratio is (
).
The point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].
How to find the ratio?To find the point that partitions segment AB in a 1:4 ratio, we can use the section formula.
Let P = (x, y) be the point that partitions segment AB in a 1:4 ratio, where AP:PB = 1:4. Then, we have:
[tex]$\frac{AP}{AB} = \frac{1}{1+4} = \frac{1}{5}$$[/tex]
and
[tex]$\frac{PB}{AB} = \frac{4}{1+4} = \frac{4}{5}$$[/tex]
Using the distance formula, we can find the lengths of AP, PB, and AB:
[tex]AP &= \sqrt{(x+3)^2 + (y-2)^2} \\PB &= \sqrt{(x-7)^2 + (y+10)^2} \\\ AB &= \sqrt{(7+3)^2 + (-10-2)^2} = \sqrt{244}[/tex]
Substituting these into the section formula, we have:
[tex]$\begin{aligned}x &= \frac{4\cdot(-3) + 1\cdot(7)}{1+4} = -1 \ y &= \frac{4\cdot2 + 1\cdot(-10)}{1+4} = -\frac{2}{5}\end{aligned}$$[/tex]
Therefore, the point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].
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Which relationships describe angles 1 and 2?
Select each correct answer.
adjacent angles
complementary angles
vertical angles
supplementary angles
Answer:
1+2=90° .so complementary angle
Find the surface area of the solid. Round your answer to the nearest tenth
if necessary.
Area of the solid composite shape with triangle and rectangle is =832cm².
Define area of composite shapes?The area of a composite shape can be determined by adding or subtracting its component pieces.
Hence, we can use two formulas:
Area of Composite Shape + Area of Composite Shape + Area of Basic Shape A (additive)
Basic Shape Area A, Basic Shape Area B, and Composite Shape Area (subtractive)
In the figure,
Dimensions of the triangle are height, h = 16cm and base, b = 12cm.
Area = 1/2 ×b ×h
= 1/2 × 16× 12
=96cm²
There are two triangles, so the total area = 96+ 96 = 192cm².
Now area of the rectangle = length × width
= 20 × 32
= 640cm².
Total area of the solid= 192 + 640 = 832cm².
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in a congressional district, 55% of the registered voters are democrats. which of the following is equivalent to the probability of getting less than 50% democrats in a random sample of size 100?
A. P( z< 50 — 55/ 100 )
B. P( z< 50 — 55/ √55(45)/100)
C. P( z< 55 — 5 / √55(45)/100)
D. P( z< 50 — 55/√100(55) (45))
The correct answer to the question, "Which of the following is equivalent to the probability of getting less than 50% democrats in a random sample of size 100?" is: B. P( z < 50 — 55/ √55(45)/100).
To find the probability, we first calculate the z-score using the formula:
z = (x - μ) / σ
where x is the value (50%), μ is the mean (55%), and σ is the standard deviation.
The standard deviation can be calculated as:
σ = √(np(1-p))
where n is the sample size (100) and p is the proportion of democrats (0.55).
Now, plug in the values into the z-score formula:
z = (50 - 55) / √(100 * 0.55 * 0.45)
The probability is then found as P(z < z-score), which is represented by the option B.
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Please help me out! Gonna be posting alot of these so if your good at this stay tuned lol but this is sophomore geometry (not advanced)
Answer: 63.8
Step-by-step explanation:
A sphere has a radius of 9in. the sphere is cut in half. what is the volume of each hemisphere. use 3.14 for pi and round to the hundredths if needed. Show work. PLEASE ANSWER IT
m/4 = 5+m/5
Find the Value of m
2x^4 −15x^3 +27x^2 +2x +8 is divided by x−4
Answer:
Step-by-step explanation:
Standard: 2x^3 - 7x^2 -x-2
Quotient: 2x^3- 7x^2 -x-2
remainder: 0
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(9x-1)º
74°
62°
PLS HURRY!!
In the given triangle, the value of x = 5.
What is a triangle's definition?
A triangle is a geometrical shape that is defined as a polygon with three sides and three angles. It is a closed figure with three line segments as its sides, and these sides intersect at three points, which are called vertices. When we add all the angles of a triangle then the result will always be 180°.
Now,
As we know the property of a triangle that
sum of all angles of triangle=180°
given angles are (9x-1)°, 74° and 62°
then,
9x-1+74+62=180°
9x+135=180
9x=45
x=5
Hence,
the value of x is 5.
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a lottery offers one $1000 prize, one $500 prize, and five $100 prizes. one thousand tickets are sold at $3 each. find the expectation if a person buys one ticket.
the expectation of buying one ticket is $2
Expectation if a person buys one ticket A person is interested in buying a ticket for a lottery that offers one $1000 prize, one $500 prize, and five $100 prizes. One thousand tickets are sold at $3 each. The expected return is calculated using the following formula:
Expectation = (Probability of winning Prize 1 × Value of Prize 1) + (Probability of winning Prize 2 × Value of Prize 2) + (Probability of winning Prize 3 × Value of Prize 3)To determine the expectation, we must first determine the probability of winning each of the three prizes.
Since one thousand tickets are sold and only one person can win the first prize, the probability of winning the $1000 prize is 1/1000 or 0.001. Similarly, the probability of winning the $500 prize is 1/1000 or 0.001. Since five $100 prizes are available and only one person can win each prize, the probability of winning any one of the five $100 prizes is 5/1000 or 0.005.
Therefore, the expectation is calculated as follows: Expectation = (0.001 × $1000) + (0.001 × $500) + (0.005 × $100)Expectation = $1 + $0.50 + $0.50Expectation = $2Thus, the expectation of buying one ticket is $2. This means that the average value of a ticket is $2, and a person can expect to win $2 on average by purchasing a ticket. Since the cost of a ticket is $3, the expected return is less than the cost of the ticket, and therefore, it is not a good investment from a financial standpoint.
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give the number of total electron groups, the number of bonding groups, and the number of lone pairs for geometry (a). express your answer as integers separated by commas.
Hence, the answer is (4, 3, 1).In conclusion The answer provided above is concise and ng factually correct, and it addresses the question directly.
In order to determine the number of total electron groups, bondiroups, and lone pairs for geometry (a), we need to use the VSEPR theory. According to this theory, the electron groups around a central atom in a molecule will arrange themselves in a way that minimizes their repulsion. The total number of electron groups includes both the bonding and lone pairs of electrons.To determine the number of electron groups for geometry (a), we first need to determine the molecular geometry of the molecule.
From the given name, we can assume that geometry (a) is tetrahedral. In a tetrahedral molecule, there are four electron groups: three bonding groups and one lone pair. Therefore, the number of total electron groups for geometry (a) is four, the number of bonding groups is three, and the number of lone pairs is one.
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write a linear equation with a slope of -7
What is the sum of A+C?  a.the matrices b -2,11,5,0,-2,1 c.12,3,1,-2,2,-1 d. -35,28,6,-1,0,12
Answer:on edge B)-2,11,5,0-2,1
The sum of the matrices A and C from the list of options is the matrix B
Calculating the sum of the matricesGiven the following matrices
Matrix A
| 0 6 2 |
| 1 5 -2 |
Matrix C
| -2 5 3 |
| -1 -7 3|
To find the sum of matrices A and C, we add the corresponding elements in each matrix:
So, we have: A + C
| 0 - 2 6 + 5 2 + 3 |
| 1 - 1 5 - 7 -2 + 3|
Evaluate the sum
| -2 11 5 |
| 0 -2 1 |
This represents option B
Therefore, the sum of matrices A and C is (B)
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Complete question
What is the sum of A+C?
Matrix A
| 0 6 2 |
| 1 5 -2 |
Matrix C
| -2 5 3 |
| -1 -7 3|
Solve the triangle please help me!!
The value of the side of the triangles are;
18. 17. 89
19. y = 9. 43, x = 5. 67
How to determine the valuesUsing the Pythagorean theorem stating that the square of the hypotenuse side is equal to the sum of the squares of the other two sides of a triangle.
From the diagram shown, we have;
21² = 11² + x²
find the squares
441 = 121 + x²
collect the like terms
x² = 320
Find the square root
x = 17. 89
To determine the value of y
sin 59 = y/11
y = 11 × 0. 8571
y = 9. 43
To determine the value of x
11² - 9. 43² = x²
x = √32.096
x = 5. 67
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Borachio eats at the same fast-food restaurant every day. Suppose the time X between the moment Borachio enters the restaurant and the moment he is served his food is normally distributed with mean 4. 2 minutes and standard deviation 1. 3 minutes. A. Find the probability that when he enters the restaurant today it will be at least 5 minutes until he is served. B. Find the probability that average time until he is served in eight randomly selected visits to the restaurant will be at least 5 minutes
The probability that when he enters the restaurant today it will be at least 5 minutes until he is served is 0.2676 and probability that average time until he is served in eight randomly selected visits is 0.0409.
The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation can be calculated as the square root of variance.
Given that mean μ = 4.2 , standard deviation σ = 1.3
1. P(X >= 5) = P((X - μ)/σ >
= (5 - 4.2) /1.3
= P(Z ≥ 0.6154)
= 1 - P(Z < 0.6154)
= 1 - 0.7324
= 0.2676
The required probability is 0.2676.
2.Given that n = 8 then [tex]\bar x[/tex] = σ/[tex]\sqrt{(n)[/tex] = 1.3/√(8) = 0.4596
P(x-bar ≥ 5) = P(([tex]\bar x[/tex] - μ)/σx-bar ≥ (5 - 4.2)/0.4596)
= P(Z ≥ 1.7406)
= 1 - P(Z < 1.7406)
= 1 - 0.9591
= 0.0409
The required probability is 0.0409.
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Write an equation that describes the function.
4. Input, x Output, Y
0 0
1 4
2 8
3 12
Answer:
Y = 4x
Step-by-step explanation:
In this equation, x represents the input value, and Y represents the output value. Coefficient 4 illustrates the rate of change or slope of the function, indicating that for every unit increase in x, the value of Y increases by four units. When x is 0, Y is also 0, consistent with the given data. Similarly, when x is 1, 2, and 3, Y is 4, 8, and 12, respectively, matching the provided output values.
What percentage of people would exed to score higher than a 2.5, but lower than 3.5? The mean: X=3.00 The SDis= + 0.500 18% 999 o 50% 03%
Therefore, approximately 68.26% of people are expected to score higher than 2.5 but lower than 3.5.
Based on the information provided, the mean (X) is 3.00 and the standard deviation (SD) is 0.50. To find the percentage of people expected to score higher than 2.5 but lower than 3.5, we will use the standard normal distribution (z-score) table.
First, we need to calculate the z-scores for both 2.5 and 3.5:
z1 =[tex] (2.5 - 3.00) / 0.50 = -1.0[/tex]
z2 = [tex](3.5 - 3.00) / 0.50 = 1.0[/tex]
Now, we can use the standard normal distribution table to find the probability of the z-scores. For z1 = -1.0, the probability is 0.1587 (15.87%). For z2 = 1.0, the probability is 0.8413 (84.13%).
To find the percentage of people expected to score between 2.5 and 3.5, subtract the probability of z1 from the probability of z2:
Percentage = [tex](0.8413 - 0.1587) x 100 = 68.26%[/tex]
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frank is building a playhouse for his daughter. the playhouse is a composite figure with a floor and no windows. what is the surface area of the playhouse? the playhouse is a rectangular prism and triangular prism.
The surface area of the playhouse is 564 square feet.
Frank is building a playhouse for his daughter.
The playhouse is a composite figure with a floor and no windows.
The playhouse is a rectangular prism and a triangular prism.
The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh,
where l is the length,
w is the width,
and h is the height.
Therefore, the surface area of the rectangular prism portion of the playhouse can be calculated by substituting the given values into the formula.
Surface area of the rectangular prism = 2lw + 2lh + 2wh
For the rectangular prism, l = 10 feet, w = 8 feet, and h = 6 feet.
Substituting the values in the formula.
Surface area of the rectangular prism
= 2lw + 2lh + 2wh
= 2 (10 feet × 8 feet) + 2 (10 feet × 6 feet) + 2 (8 feet × 6 feet)
= 160 feet2 + 120 feet2 + 96 feet2= 376 feet2
The surface area of the rectangular prism of the playhouse is 376 square feet.
The formula for the surface area of a triangular prism is 2lw + lh + ph,
where l is the length, w is the width, h is the height, and p is the slant height.
Therefore, the surface area of the triangular prism portion of the playhouse can be calculated by substituting the given values into the formula.
Surface area of the triangular prism = 2lw + lh + ph
For the triangular prism, l = 8 feet, w = 5 feet, h = 6 feet, and p = 10 feet.
Substituting the values in the formula.
Surface area of the triangular prism = 2lw + lh + ph= 2 (8 feet × 5 feet) + (8 feet × 6 feet) + (10 feet × 6 feet)= 80 feet2 + 48 feet2 + 60 feet2= 188 feet2
The surface area of the triangular prism of the playhouse is 188 square feet.
The total surface area of the playhouse can be found by adding the surface area of the rectangular prism and the surface area of the triangular prism.
Surface area of the playhouse = surface area of rectangular prism + surface area of triangular prism.
= 376 square feet + 188 square feet
= 564 square feet.
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What is the area of this parallelogram?
O A = 20 ft²
O A=213ft²
O A = 33 ft²
O A=41 ft²
5 ft
4 ft
81 ft
The area of the given parallelogram is A- 33(1/2) ft² using the base and height of the parallelogram. the correct answer is (c).
What is a parallelogram?A quadrilateral with two sets of analogous edges is appertained to as a parallelogram. In a parallelogram, the opposing edges are of equal length, and the opposing angles are of equal size. also, the internal angles that are supplementary to the transversal on the same side. 360 ° is the sum of all internal angles. A parallelepiped is a three- dimensional shape with parallelogram- shaped sides. The base( one of the analogous lines) and height( the distance from top to bottom) of the parallelogram determine its area. A parallelogram's border is determined by the lengths of its four edges. The characteristics of a parallelogram are participated by the shapes of a square and cell. What's area? The size of a section on a face is determined by its area. face area refers to the area of an open face or the border of a three- dimensional object, whereas the area of an area area plane region or area area plane area refers to the area of a shape or planar lamella.
The area of a parallelogram is given by
[tex]base*height.base=8(1/3)ft[/tex]
height=4ft
[tex]Area=b*h =(25/3)*4 =100/3 = 33[/tex]
[tex][base]\frac{1}{3}[(hieght)] ft^{2}[/tex]
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I Really want this pleaseeeeeeeeeeeeeeeeeee
Answer:
no
Step-by-step explanation:
using Pythagorean theorem:
[tex]26^{2} +42^{2}=50^{2}[/tex]
676+1764=2500
2440=2500
2440<2500
Answer:no
Mr. Kha Lipat wants to earn 8% on his investment. How much money should he invest today in order to receive 400. 00 one year from now?
Mr. Kha Lipat should invest $5,000 today in order to receive $400.00 in interest one year from now at an 8% interest rate.
To calculate how much money Mr. Kha Lipat should invest today to receive $400.00 one year from now at an 8% interest rate, we can use the formula for calculating simple interest though compound intrest:
I = P * r * t
where I is the interest earned, P is the principal (the initial amount invested), r is the interest rate (as a decimal), and t is the time period (in years).
We know that Mr. Kha Lipat wants to earn $400.00 in interest, the interest rate is 8% or 0.08 (as a decimal), and the time period is 1 year. We can plug these values into the formula and solve for P:
I = P * r * t
400 = P * 0.08 * 1
400 = 0.08P
P = 400 / 0.08
P = 5000
Therefore, Mr. Kha Lipat should invest $5,000 today in order to receive $400.00 in interest one year from now at an 8% interest rate.
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number 5 goes through the device and the result is 25 . what would a possible rule for machine B be ?
Answer: multiplied by 5 or squared
Step-by-step explanation:
If the number 5 goes in and 25 is the result, the rule could be multiplying by 5 or squaring the number that goes in (input).
5 x 5 = 25
5^2 = 25.
Write the linear equation in standard form y=19/14x+13
The linear equation in standard form is 19x - 14y = -182.
What is Linear equation?
A linear equation is a mathematical equation that describes a straight line on a graph. In other words, it is an equation that relates a variable or variables to a constant through a linear function, where the highest power of the variable is one. A general form of a linear equation is:
y = mx + b
To write the linear equation in standard form Ax + By = C, where A, B, and C are integers and A is positive, we need to get rid of the fraction in the equation.
To do this, we can multiply both sides of the equation by the denominator of the fraction, which is 14. This gives:
14y = 19x + 182
Next, we can rearrange this equation by subtracting 19x from both sides:
-19x + 14y = 182
Finally, we can multiply both sides of the equation by -1 to make the coefficient of x positive:
19x - 14y = -182
So, the linear equation in standard form is 19x - 14y = -182.
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Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures whenever appropriate. (Do this on paper. Your instructor may ask you to turn in this work.)
(a) P(0Image for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneveZImage for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneve2.74)
(b) P(0Image for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneveZImage for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneve1)
(c) P(-2.40Image for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneveZImage for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneve0)
(d) P(-2.40Image for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneveZImage for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneve+2.40)
(e) P(ZImage for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneve1.63)
(f) P(-1.74Image for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneveZ)
(g) P(-1.4Image for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneveZImage for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneve2.00)
(h) P(1.63Image for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneveZImage for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneve2.50)
(a) To find P(0 < Z < 2.74), you'll want to look up the z-score for 2.74 in a standard normal table or use a calculator with a built-in normal distribution function. The probability is the area under the curve between 0 and 2.74.
(b) To find P(0 < Z < 1), you'll look up the z-score for 1 in a standard normal table or use a calculator. The probability is the area under the curve between 0 and 1.
(c) To find P(-2.40 < Z < 0), you'll look up the z-score for -2.40 in a standard normal table or use a calculator. The probability is the area under the curve between -2.40 and 0.
(d) To find P(-2.40 < Z < 2.40), you can first calculate the probability for P(-2.40 < Z < 0) and P(0 < Z < 2.40), and then sum the two probabilities.
(e) To find P(Z > 1.63), look up the z-score for 1.63 in a standard normal table or use a calculator. The probability is the area under the curve to the right of 1.63.
(f) To find P(Z < -1.74), look up the z-score for -1.74 in a standard normal table or use a calculator. The probability is the area under the curve to the left of -1.74.
(g) To find P(-1.4 < Z < 2.00), first look up the z-scores for -1.4 and 2.00 in a standard normal table or use a calculator. Subtract the smaller probability from the larger probability to find the area under the curve between these two values.
(h) To find P(1.63 < Z < 2.50), first look up the z-scores for 1.63 and 2.50 in a standard normal table or use a calculator. Subtract the smaller probability from the larger probability to find the area under the curve between these two values.
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At a basketball game, a team made 53 successful shots. They were a combination of 1- and 2-point shots. The team scored 90 points in all. Write and solve a system of equations to find the number of each type of shot.
Answer: the team amassed 88i points total, by shooting t two-point baskets and u 1-point free throws.
t+u = 53
total is: 2t + u = 88.
Step-by-step explanation:
hope i makes sense
Write ^4√11^5 without radicals.
Answer: ^4√11^5 = 11^(5/4)
Step-by-step explanation: When we apply a radical, we are asking what number, when raised to a certain power, gives us the number under the radical. For example, ^4√16 is asking what number, when raised to the fourth power, gives us 16. The answer is 2, since 2^4 = 16.
So, ^4√11^5 is asking what number, when raised to the fourth power, gives us 11^5. We can simplify this expression using the exponent laws:
^4√11^5 = (11^5)^(1/4) = 11^(5/4)
Therefore, the simplified expression for ^4√11^5 is 11^(5/4). This expression does not have any radicals, making it easier to work with and manipulate.
Hope this helps, and have a great day!