4. Ilaria earned 86 on her statistics midterm and 82 on her chemistry midterm. In the statistics class the mean score was 80 with standard deviation 4. In the chemistry class the mean score was 70 with standard deviation 6. (6 pts) a. Convert each midterm score to a standard z score. b. On which test did Ilaria do better, relative to the rest of the class?
Answers
Ilaria earned an 86 on her statistics midterm and 82 on her chemistry midterm.
a. Z-score for Statistics midterm = z = (X - μ) / σ Z = (86 - 80) / 4 Z = 1.5 Z-score for Chemistry midterm = z = (X - μ) / σ Z = (82 - 70) / 6 Z = 2.
b. Ilaria performed better on the chemistry midterm relative to the rest of the class than she did on the statistics midterm relative to the rest of the class.
a. Z-score for Statistics midterm = z = (X - μ) / σZ = (86 - 80) / 4Z = 1.5Z-score for Chemistry midterm = z = (X - μ) / σZ = (82 - 70) / 6Z = 2.
b. To determine on which test Ilaria did better, relative to the rest of the class, we have to compare the two z-scores. We can do this by looking at the standardized value or z-score.
Since z-scores have a mean of 0 and a standard deviation of 1, we can compare z-scores from different distributions. The z-score for the chemistry midterm is higher than the z-score for the statistics midterm.
This means that Ilaria performed better on the chemistry midterm relative to the rest of the class than she did on the statistics midterm relative to the rest of the class.
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Related Questions
Nina owns a condominium where she paid $3,340 in maintenance fees this year. If her property taxes are 15% of this amount, how much did Nina pay in property taxes?
Answers
Nina pay in property taxes 501. or \(5.01*10^{2}\).
A property tax, often known as a millage rate, is an ad valorem tax based on a property's value. The tax is imposed by the administrative body of the region where the property is situated. This could be the federal government, a federated state, a county, a region of land, or a municipality. The average effective property tax rate in the Lone Star State is 1.60%, making Texas' property taxes the seventh-highest in the nation. Comparing that to the current 0.99% national average will help. Property taxes in Texas cost the average homeowner $3,797 a year. It is well known that British property owners do not pay property tax. But hold on, it's too soon to celebrate because there might still be taxes to pay.
Based on the given conditions, formulate:
3340*15%
Calculate.
501
Alternative forms.
\(5.01*10^{2}\)
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Plzzzzzzzzzzzz help!!!!!!!
Write an expression for the sequence of operations described below.
raise the difference of 2 and q to the 8th power
Do not simplify any part of the expression.
Answers
Answer:
Step-by-step explanation:
Difference of 2 and q: 2 - q
Expression: (2 - q)⁸
Question 3 The bus impedance matrix of a four-bus network with values in per unit is j0.15 j0.08j0.04 j0.07 j0.08 j0.15 j0.06j0.09 Z bus j0.04 j0.06 j0.13 j0.05 j0.07 j0.09 j0.05 j0.12 have their subtransient reactances Generators connected to buses and included in Zbus. If prefault current is neglected, find the subtransient current in per unit in the fault for a three-phase fault on bus 4. Assume the voltage at the fault is 1.0/0° per unit before the fault occurs. Find also the per-unit current from generator 2, whose subtransient reactance is 0.2 per unit. =
Answers
To find the subtransient current in per unit for a three-phase fault on bus 4, we need to calculate the fault current using the bus impedance matrix.
Given bus impedance matrix Zbus:
| j0.15 j0.08 j0.04 j0.07 |
| j0.08 j0.15 j0.06 j0.09 |
| j0.04 j0.06 j0.13 j0.05 |
| j0.07 j0.09 j0.05 j0.12 |
To find the fault current on bus 4, we need to find the inverse of the Zbus matrix and multiply it by the pre-fault voltage vector.
The pre-fault voltage vector V_pre-fault is given as:
| 1.0/0° |
| 1.0/0° |
| 1.0/0° |
| 1.0/0° |
Let's calculate the inverse of the Zbus matrix:
Zbus_inverse = inv(Zbus)
Now, we can calculate the fault current using the formula:
I_fault = Zbus_inverse * V_pre-fault
Calculating the fault current, we have:
I_fault = Zbus_inverse * V_pre-fault
Substituting the values and calculating the product, we get:
I_fault = Zbus_inverse * V_pre-fault
= Zbus_inverse * | 1.0/0° |
| 1.0/0° |
| 1.0/0° |
| 1.0/0° |
Please provide the values of the Zbus matrix and the pre-fault voltage vector to obtain the specific values for the fault current and the per-unit current from generator 2.
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Solve for x. Enter the solutions from least to greatest. x^2 +7=43
Answers
Answer:
x = - 6, x = 6
Step-by-step explanation:
Given
x² + 7 = 43 ( subtract 7 from both sides )
x² = 36 ( take the square root of both sides )
x = ± \(\sqrt{36}\) = ± 6
Thus
x = - 6, x = 6
Answer:
x exponent 2=43-7
x^2=36
x=6
Step-by-step explanation:
The most important component of a physical structure is a solid foundation on which the rest of the structure sits. a strong foundation allows buildings to last longer and withstand many outside forces. just like the foundation of a building, a strong foundation for algebra is critical for success and allows you to extend your understanding to more complex mathematical and real-world situations. what are some of the foundational, or key, concepts of algebra that you’ve learned so far?
Answers
The foundational concept of algebra is to use the alphabetical letters to find the unknown number.
Algebra is the concept that uses the alphabetical letters such as x, y, z, etc. to calculate the unknow numbers. here the letters are also called as variables. The values that are known in the expression as termed as constants.
The general operations performed on the algebra is
Addition = x + ySubtraction = x - yMultiplication = x * yDivision = x / yHere the alphabets x and y are called variables.
Order of operations:
The order of operation in algebra is given as follows
Perform all the operations inside the bracketsPerform the operations on roots and exponentsPerform all the division and multiplication operations moving from left to rightPerform all the addition and subtraction operations from left to right.To know mire about Algebra here
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what is the amount of 839k in thousands
Answers
what is the answer to: 7 2/3 + 2 1/5 =
Answers
Answer: 9 13/15
Step-by-step explanation:
There are children in a play the ratio of 1;1 the ratio of girls who csan sing to girls who cant sing is 1;1 8 girls can sing
Answers
Answer:
8 girsl can sing
8 girls cannot sing
Total number of girls = 16
Step-by-step explanation:
The ratio of girls who csan sing to girls who cant sing is 1:1
Which means the number of girls who can sing and cannot sing are equal .
IF the number of girls who can sing is 8 then the number of girls who cant sing is also 8.
8:8
Dividing both sides by 8 gives
1:1
The total number of girls would be (8+8= )16.
Jack is standing on the ground talking on his mobile phone. He notices a plane flying at an altitude of
2400 metres. If the angle of elevation to the plane is 70° and by the end of his phone call it has an angle
of elevation of 50°, determine the distance the plane has flown during Jack’s phone call - use the cosine rule
Answers
Using the cosine rule, the distance the plane has flown during Jack's phone call can be calculated by taking the square root of the sum of the squares of the initial and final distances, minus twice their product, multiplied by the cosine of the angle difference.
To determine the distance the plane has flown during Jack's phone call, we can use the cosine rule in trigonometry.
The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.
Let's denote the initial distance from Jack to the plane as d1 and the final distance as d2.
We know that the altitude of the plane remains constant at 2400 meters.
According to the cosine rule:
\(d^2 = a^2 + b^2 - 2ab \times cos(C)\)
Where d is the side opposite to the angle C, and a and b are the other two sides of the triangle.
For the initial angle of elevation (70°), we have the equation:
\(d1^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \timescos(70)\)
Similarly, for the final angle of elevation (50°), we have:
\(d2^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \times cos(50)\)
To find the distance the plane has flown, we subtract the two equations:
\(d2^2 - d1^2 = 2 \times 2400 \times a \times (cos(70) - cos(50))\)
Now we can solve this equation to find the value of a, which represents the distance the plane has flown.
Finally, we calculate the square root of \(a^2\) to find the distance in meters.
It's important to note that the angle of elevation assumes a straight-line path for the plane's movement and does not account for any changes in altitude or course adjustments that might occur during the phone call.
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Match the term on the right with its image or description on the left. (6 points)
1.
Circle A and a line segment connecting points B and C which are on the circle.
2.
Circle A and point B on the circle and line passes through point B only.
3.
a segment between the center of a circle and a point on the circle
4.
the distance around a circle
5.
the distance along a circle between two points on the circle
6.
Circle A and a line segment connecting points B and C which are on the circle.
a.
Secant
b.
Radius
c.
Circumference
d.
Chord
e.
Tangent
f.
Arc length
Answers
Answer:
See explanation
Step-by-step explanation:
Match the term on the right with its image or description on the left. (6 points)
check
1.
Circle A and a line segment connecting points B and C which are on the circle.
answer: Secant
2.
Circle A and point B on the circle and line passes through point B only.
answer: Tangent
3.
the distance along a circle between two points on the circle
Answer: Arc length
4.
the distance around a circle
Answer: Circumference
5.
a segment between the center of a circle and a point on the circle
Answer: Radius
6.
Circle A and a line segment connecting points B and C which are on the Answer:Chord
I just took the quiz and came back to help you!
Have a great day!!
The statements along with the blanks are given above.
What is a circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center.
Given is the image or description and terms w.r.t a circle.
Circle A and a line segment connecting points B and C which are on the circle : Chord.Circle A and point B on the circle and line passes through point B only : Secant.A segment between the center of a circle and a point on the circle : Radius.The distance around a circle : Circumference.The distance along a circle between two points on the circle : Arc length.Therefore, the statements along with the blanks are given above.
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The equation $y = -16t^2 + 28t + 144$ describes the height $y$ (in feet) at time $t$ (in seconds) of a ball tossed up in the air at $28$ feet per second from a height of $144$ feet from the ground. In how many seconds will the ball hit the ground?
Answers
Answer:
4 seconds
Step-by-step explanation:
Given the equation y = -16t² +28t +144 describes a ball's height as a function of time in seconds, you want to know when the ball will hit the ground.
ZeroThe ball will hit the ground when the value of y is zero.
0 = -16t² +28t +144
t² -7/4t -9 = 0 . . . . . divide by 16
t² -7/4t +(7/8)² = 9 +(7/8)² . . . . . complete the square
t = 7/8 +√(9 49/64) = 7/8 +3 1/8 = 4 . . . . take the square root, add 7/8
The ball will hit the ground after 4 seconds.
1) Lesson 9 Practice Problems An image of a book shown on a website is 1.5 inches wide and 3 inches tall on a computer monitor. The actual book is 9 inches wide. a. What scale is being used for the image? b. How tall is the actual book? Show your work.
Answers
We have:
Image of book on website
Wide = 1.5 inches
Tall = 3 inches
Actual book
Wide = 9 inches
Tall = ?
a) Scale used for the image:
\(\frac{wide\text{ actual book}}{wide\text{ image book}}=\frac{9}{1.5}=6\)Answer: scale = 6 inches
b) Tall actual book
\(\text{tall image book }\times scale=3\times6=18\)Answer: tall = 18 inches
Two carts, A and B, are connected by a rope 39ft long that passes over a pulley P. The point Q is on the floor 12ft directly beneath P and between the carts. Cart A is being pused away from Q at a speed of 3 fuls. How fast (in f is 6 is cart B moving toward Q at the instant when cart A is 5 ft from Q ? (Round your answer to two decimal places.) ft/s
Answers
At the given instant, when cart A is 5 ft from Q, cart B is moving toward Q at a speed of approximately 0.388 ft/s. To solve this problem, we can use the concept of related rates.
Let's denote the distance between cart A and the pulley P as x, and the distance between cart B and the pulley P as y.
At the given instant, we are given that cart A is moving away from Q at a speed of 3 ft/s. This means that the rate of change of x with respect to time (dx/dt) is 3 ft/s.
We are asked to find the rate at which cart B is moving toward Q at this instant, which is the rate of change of y with respect to time (dy/dt).
From the given information, we can form a right triangle with sides x, y, and the rope length of 39 ft. By applying the Pythagorean theorem, we have:
x^2 + y^2 = 39^2
Differentiating this equation implicitly with respect to time t, we get:
2x(dx/dt) + 2y(dy/dt) = 0
Substituting the known values, we have:
2(5)(3) + 2y(dy/dt) = 0 [At the instant when cart A is 5 ft from Q, x = 5]
30 + 2y(dy/dt) = 0
Simplifying the equation, we can solve for dy/dt:
2y(dy/dt) = -30
dy/dt = -30 / (2y)
To find y, we can use the right triangle formed by x, y, and the rope length:
x^2 + y^2 = 39^2
5^2 + y^2 = 1521
y^2 = 1521 - 25
y = √1496
y ≈ 38.68 ft
Now we can substitute this value of y into the equation to find dy/dt:
dy/dt = -30 / (2 * 38.68)
dy/dt ≈ -0.388 ft/s
Therefore, at the instant when cart A is 5 ft from Q, cart B is moving toward Q at a rate of approximately 0.388 ft/s.
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Pls explain how you got the answers
Answers
Answer:
1. 2.64172
2. 9.94194
3. 76.2
4. 10.9728
5. 49.2126
6. 443.603
7. 402.336
8. 259.08
9. 328.084
10. 7.57082
11. 7.25748
12. 55.1156
13. 127
14. 22.7125
15. 189.598
Step-by-step explanation:
1. liters to gallons 1:0.264172
10 L = 2.64172 gal.
2. kilometers to miles 1:0.621371
16 Km = 9.94194 mil.
3. inches to centimeters 1:2.54
30 in = 76.2 cm
4. yards to meters 1:0.9144
12 yd. = 10.9728 m
5. meters to feet 1:3.28084
15 m = 49.2126 ft
6. fluid ounces to milliliters 1:29.5735
15 fl oz = 443.603 mL
7. miles to kilometers 1:1.60934
250 mi = 402.336 km
8. feet to meters 1:0.3048
850 ft = 259.08 m
9. meters to feet (see problem 5)
100 m = 328.084 ft
10. quarts to liters 1:0.946353
8 qt = 7.57082 L
11. pounds to kilograms 1:0.453592
16 lbs = 7.25748 kg
12. kilograms to pounds 1:2.20462
25 kg = 55.1156 lbs
13. inches to centimeters (see problem 3)
50 in = 127 cm
14. gallons to liters 1:3.78541
6 gal = 22.7125 L
15. kilograms to pounds (see problem 12)
86 kg = 189.598 lbs
In a certain lottery game, the chance of getting a winning ticket is exactly one in a thousand. suppose a person buys one ticket each day (except on the leap year day february 29) over a period of fifty years. what is the expected number e[t] of winning tickets in fifty years
Answers
The expected number of winning tickets in fifty years is 18.25.
The expected value of binomial distribution:If there is a series of n independent Bernoulli trials, then each of the trials will have a probability of success i.e p. The expected value of the binomial distribution E( n, p) is the product of n and p
=> E(n, p) = np
Using the above formula we will solve given problem given below
Here we have
In a certain lottery game, the chance of getting a winning ticket is exactly one in a thousand i.e p = [ 1/1000]
Given that a person buys one ticket each day (except on the leap year day February 29) over a period of fifty years.
As we know 1 year = 365
No of tickets that can be bought in fifty years (n)= 50 × 365 = 18250
Given that, the chance of winning = [ 1/1000] = 0.001
=> p = 0.001
Chance of winning 50 years = 18250 × 0.001 = 18.25
Therefore,
The expected number of winning tickets in fifty years is 18.25.
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The weight of the items in a truck is ton.
How many pounds do the items in the
truck weigh?
Answers
[3 points] The probability that an electronic component will fail in performance is 0.1. Use the normal approximation to Binomial to find the probability that among 100 such components, (a) at least 12 will fail in performance. (b) between 8 and 13 (inclusive) will fail in performance. (c) Exactly 9 will fail in performance. [Hint: You are approximating Binomial with normal distribution.]
Answers
Here are the steps to calculate the probabilities for the given questions: Given, Probability that an electronic component will fail in performance p = 0.1And, the total number of components n = 100 Therefore, the number of components that will fail in performance X ~ Binomial (n, p)i.e., X ~ B (100, 0.1)
Note: By normal approximation to Binomial distribution, it means that the binomial distribution can be approximated to normal distribution by taking μ = np and σ² = npq and applying the continuity correction factor while calculating probabilities.
A) At least 12 will fail in performance The probability of at least 12 electronic components failing in performance P(X ≥ 12) is calculated as follows: P(X ≥ 12) = P(Z ≥ (11.5-10)/2.97) -- applying continuity correction factor= P(Z ≥ 0.51) -- rounding to 2 decimal places= 1 - P(Z < 0.51)= 1 - 0.695 = 0.305Therefore, the probability of at least 12 components failing in performance is 0.305.
B) Between 8 and 13 (inclusive) will fail in performance. The probability that between 8 and 13 components fail in performance P(8 ≤ X ≤ 13) is calculated as follows: P(8 ≤ X ≤ 13) = P(Z ≤ (13.5-10)/2.97) - P(Z ≤ (7.5-10)/2.97) -- applying continuity correction factor= P(Z ≤ 1.02) - P(Z ≤ -1.02) -- rounding to 2 decimal places= 0.846 - 0.154= 0.692. Therefore, the probability that between 8 and 13 components fail in performance is 0.692.
C) Exactly 9 will fail in performance. The probability that exactly 9 components will fail in performance P(X = 9) is calculated as follows: P(X = 9) = P(8.5 ≤ X ≤ 9.5) -- applying continuity correction factor= P(Z ≤ (9.5-10)/2.97) - P(Z ≤ (8.5-10)/2.97)= P(Z ≤ -0.17) - P(Z ≤ -1.02)= 0.432 - 0.154= 0.278
Therefore, the probability that exactly 9 components will fail in performance is 0.278.Therefore, the probabilities that were asked for are:At least 12 will fail in performance - 0.305Between 8 and 13 (inclusive) will fail in performance - 0.692Exactly 9 will fail in performance - 0.278
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I NEED THE ANSWER ASAP
Answers
Answer:
x = 5
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
21x + 5 is an exterior angle of the triangle , then
21x + 5 = 5 + 13x + 40
21x + 5 = 13x + 45 ( subtract 13x from both sides )
8x + 5 = 45 ( subtract 5 from both sides )
8x = 40 ( divide both sides by 8 )
x = 5
Answer:
x=5
Step-by-step explanation:
Angles Q and R are supplementary
13x + 21x +5 = 180
10+34x =180
34x=170
x = 5
A. The vertical scale is too high.
B. The vertical scale should not start at zero.
C. The bars are not the same width.
D. The bars are not the same height.
Answers
what is the value of the expression (a^3 + b^0)^2 where a = -2 b = 4 ?
Answers
Answer:
1938
Step-by-step explanation:
ITIS BECAUS.....SJFJCJAJ WHER FICOAK WERE KFKCKA
Answer:
When a = -2 and b = 4, this expression is equal to 49
Step-by-step explanation:
You can solve this by simply plugging in the given values and solving:
((-2)³ + 4⁰)²
= (-8 + 1)²
= -7²
= 49
A plane travels a distance of 17,000 km in a time of 2.4 hours.
What is its average speed rounded to the nearest whole number?
Answers
Answer:
7083 KM/H
Step-by-step explanation:
17000 / 2.4 = 7083 (Plus some decimals, but rounded up its 7083.)
\(4(x^{3} -3x-2)\)
factor completely
Answers
Answer:
bgreewqazxcvbnmmmmmmmmm,,,,lpoiuytrewqasdfghjkl
Step-by-step explanation:
mmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
Order each set of numbers from least to greatest
1.\(\sqrt{200}\), 14, \(\frac{41}{3}\)
Answers
Answer:
41/3, 14, square root of 200
Step-by-step explanation:
41/3 = 13.66
14 is just 14
and square root of 200 is 14.14
Order each step and justification that is needed to solve the equation below. -2x = 28 - 6x Steps Justifications -2r = 28 - 61 Given - 2x + 6r 28 - 61 + 61 Simplification Simplification Division property of equality -41 28 28 4 r = 7 r = - 7 4r = 28 - 4x = 28 Addition property of equally
Answers
-2x = 28 - 6x --------------------------> Given
-2x + 6x = 28 - 6x + 6x------------------------------>Addition property of equality
4x = 28 -----------------------------------------> Simplification
4x/4 = 28/4 --------------------------------->Division property of equality
x = 7 --------------------------------------->Simplification
How do you simplify expressions with rational exponents
Answers
Answer:
Step-by-step explanation:
Simplify expression with rational exponents can look like a huge thing when you first see them with those fractions sitting up there in the exponent but let's remember our properties for dealing with exponents. We can apply those with fractions as well.
Examples
(a) \((p^4)^{\dfrac{3}{2}}\)
From above, we have a power to a power, so, we can think of multiplying the exponents.
i.e.
\((p^{^ {\dfrac{4}{1}}})^{\dfrac{3}{2}}\)
\((p^{^ {\dfrac{12}{2}}})\)
Let's recall that when we are dealing with exponents that are fractions, we can simplify them just like normal fractions.
SO;
\((p^{^ {\dfrac{12}{2}}})\)
\(= (p^{ 6})\)
Let's take a look at another example
\(\Bigg (27x^{^\Big{6}} \Bigg) ^{{\dfrac{5}{3}}}\)
Here, we apply the \(\dfrac{5}{3}\) to both 27 and \(x^6\)
\(= \Bigg (27^{{\dfrac{5}{3}}} \times x^\Big{\dfrac{6}{1}\times {{\dfrac{5}{3}}} }\Bigg)\)
\(= \Bigg (27^{{\dfrac{5}{3}}} \times x^\Big{\dfrac{2}{1}\times {{\dfrac{5}{1}}} }\Bigg)\)
Let us recall that in the rational exponent, the denominator is the root and the numerator is the exponent of such a particular number.
∴
\(= \Bigg (\sqrt[3]{27}^{5} \times x^{10} }\Bigg)\)
\(= \Bigg (3^{5} \times x^{10} }\Bigg)\)
\(= 249x^{10}\)
3x^3(4x^4)=?
i need this plz
Answers
Answer:
12x^7.
Step-by-step explanation:
3x^3(4x^4)=
3*4 * x^(3+4)
= 12x^7.
-6(2x+3)=-12x-18
plz help i will give you braneset
Answers
Answer:
-6(2 x + 3) =-12 x-18 = 0 (after you simplify) :)
Step-by-step explanation:
Given x=3;y= -2 determine the value of the expression
Answers
what is the expression we need to determine the value of ?
Question 1(Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Approximate pi plus the square root of 70 to the nearest hundredth.
8.37
11.14
11.51
12.14
Question 2(Multiple Choice Worth 2 points)
(Irrational Numbers LC)
Describe in words where the square root of forty-eight would be plotted on the number line.
Between 7 and 8, but closer to 7
Between 7 and 8, but closer to 8
Between 6 and 7, but closer to 6
Between 6 and 7, but closer to 7
Question 3(Multiple Choice Worth 2 points)
(Irrational Numbers LC)
Which of the following numbers are irrational?
negative four and 8237 ten thousandths, one half pi, cube root of four, and four plus the square root of twenty-five
one half pi and the cube root of four
−4.8237 and four plus the square root of twenty-five
−4.8237 and one half pi
the cube root of four and four plus the square root of twenty-five
Question 4(Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Compare square root of one hundred fifty and one hundred fourteen ninths using <, >, or =.
square root of one hundred fifty > one hundred fourteen ninths
square root of one hundred fifty = one hundred fourteen ninths
one hundred fourteen ninths < square root of one hundred fifty
one hundred fourteen ninths > square root of one hundred fifty
Question 5(Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Identify the location of the values square root of 11, square root of 8, and twenty two ninths on the number line.
Number line with points plotted at two and four tenths labeled Point A, two and eight tenths labeled Point B, and three and three tenths labeled Point C.
Point A is square root of 11, point B is square root of 8, and point C is twenty-two ninths.
Point A is twenty-two ninths, point B is square root of 8, and point C is square root of 11.
Point A is twenty-two ninths, point B is square root of 11, and point C is square root of 8.
Point A is square root of 11, point B is twenty-two ninths, and point C is square root of 8.
Question 6(Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Approximate negative eight plus the square root of twenty to the nearest tenth.
4.5
3.5
−3.5
−4.5
Answers
The computation shows that pi plus the square root of 70 to the nearest hundredth will be C. 11.51
How to compute the value?From the information, we are told to pi plus the square root of 70 to the nearest hundredth. This will be:
= π + ✓70
= 3.14 + 8.37
= 11.51
The description in words where the square root of forty-eight would be plotted on the number line will be between 6 and 7, but closer to 7.
Lastly, it should be noted that square root of one hundred fifty > one hundred fourteen ninths.
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Find the circumference of this circle using 3 for π.
Answers
The circumference of the circle is 30 cm.
What is circumference measured in?Any unit for measuring length can be used to calculate the circumference, including feet, miles, metres, millimetres, etc.
By substituting 3 for, we can use the following formula to determine the circle's circumference:
C = 2πr
where r is the radius and C is the circumference.
We can observe from the provided diagram that the circle's radius is 5 cm. Thus, by changing r = 5 cm and = 3 in the formula, we obtain:
C = 2(3)(5) = 30
The circle's circumference is 30 cm as a result.
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