A national achievement test is administered annually to 3rd graders. the test has a mean score of 100 and a standard deviation of 15. if jane's z-score is 1.20, what was her score on the test?
Answer:
118.
Step-by-step explanation:
To find Jane's score on the national achievement test with a given mean of 100 and standard deviation of 15, we calculate it using her z-score of 1.20 to get her score of 118.
Explanation:The question asks: A national achievement test is administered annually to 3rd graders. The test has a mean score of 100 and a standard deviation of 15. If Jane's z-score is 1.20, what was her score on the test.
To find Jane score on the test, we use the formula for calculating scores from z-scores: Score = Mean + (Z-score × Standard Deviation).
Given that the mean is 100 and the standard deviation is 15, and Jane's z-score is 1.20, we can calculate her score as follows:
Score = 100 + (1.20 × 15)Score = 100 + 18Score = 118Therefore, Jane's score on the national achievement test was 118.
3-5x in verbal expression
The sum of three consecutive even integers is 378. what is the largest of the three integers
The largest of the three integers is 127.
It is required to find the largest of the three integers.
What is integer?An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
Given that:
Let's assume, that first number is "x", than second number will be "x + 1" and third one is "x + 2".
x + (x + 1) + (x + 2) = 378
x + x + 1 + x + 2 = 378
3x + 3 = 378
3(x + 1) = 378
Divide by 3
x + 1 = 126
x = 125
The first number is 125, second number is 126 and third number is 127.
So, the largest of the three integers is 127.
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how do i find the degree of x and y?
Which is the best estimate of -14 1/9 (-2 9/10)
please help thank you very much.
How do I find the domain of a function
The domain of a function is the set of all possible input values that can be inserted into the function. The domain can be numerical or non-numerical, depending on what the function describes.
Explanation:In mathematics, finding the domain of a function involves identifying all possible values that can be inserted into the function. A function's domain can be a set of numerical values or a set of non-numerical values.
For example, if we have a function based on majors at a university, the domain could take form as X = {English, Mathematics, ...}, i.e., a list of all the majors offered at the university, plus undeclared, which are all possible inputs into the function.
Similarly, if we have a random variable X = hair color, then the domain of X would include all possible hair colors.
If the function is based on numerical variables, such as a Quadratic Function, the domain would be the set of all real numbers. For instance, the domain of Y = {0, 1, 2, ...} consists of the integers from zero up to a certain limit. Generally, the domain of a function is the set of all possible input values that will produce a value in the function.
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The temperature in a town is 36.6F during the day and -12.6F at night what is the temperature change from day to night
The temperature changes by 49.2F from day to night. You calculate this by subtracting the night temperature from the day temperature and remembering to treat subtraction of a negative as addition.
Explanation:The subject of your question is the calculation of temperature change, which is a simple subtraction problem in mathematics. Given a temperature of 36.6F during the day and a temperature of -12.6F at night, you can find the temperature change by subtracting the night temperature from the day temperature.
So, it will be 36.6F - (-12.6F) equals 49.2F. It's important to note here that subtracting a negative number is the same as adding a positive number which is why we add 12.6F instead of subtracting it.
This means, the temperature changes by 49.2F from day to night.
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A group of students is counting the number of plastic bags placed in a landfill during a single day .What are the students doing?
A)collecting data
B)Drawing a conclusion
C)Stating a problem
D)Making a hypothesis
Answer:
A
Step-by-step explanation:
Name two congruent angles that measure 15
What is the sum of the polynomials? ( 8x^2 -9y^2-4x) + (x^2- 3y^2- 7x) answer options are in the pics
Answer: The correct option is (D) [tex]9x^2-12y^2-11x.[/tex]
Step-by-step explanation: We are given to find the following sum of the polynomials :
[tex]S=(8x^2-9y^2-4x)+(x^2-3y^2-7x)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the required sum, we need to add the coefficients of the same unknown variables with equal powers.
The sum of the polynomials in (i) is as follows :
[tex]S\\\\=(8x^2-9y^2-4x)+(x^2-3y^2-7x)\\\\=8x^2-9y^2-4x+x^2-3y^2-7x\\\\=(8+1)x^2-(9+3)y^2-(4+7)x\\\\=9x^2-12y^2-11x.[/tex]
Thus, the required sum of the polynomials is [tex]9x^2-12y^2-11x.[/tex]
Option (D) is CORRECT.
The ratio of men to women working for a company is 7 to 5 . if there are 105 men working for the company, what is the total number of employees?
15/16 × 5/6
Reduce your answers to simplest form
Give three solutions to the equation y = 3 x + 4 y=3x+4 . give your solutions as ordered pairs, using reduced fractions or integers for coordinates.
Final answer:
To find three solutions to the equation y = 3x + 4, you can choose different values for x and calculate the corresponding values of y. Three solutions are (0, 4), (1, 7), and (-1, 1).
Explanation:
The equation y = 3x + 4 represents a linear equation in slope-intercept form, where the coefficient of x is the slope and the constant term is the y-intercept. To find three solutions to this equation, we can choose different values for x and calculate the corresponding values of y.
If x = 0, then y = 4. So one solution is (0, 4).If x = 1, then y = 7. So another solution is (1, 7).If x = -1, then y = 1. So the third solution is (-1, 1).Kim has small wooden cube shaped blocks. To make the next size cube, she needs 8 blocks. Write a sequence to show the number of blocks needed for each increasingly larger cube. Include at least 6 terms in the sequence.
A builder wants to build a diagonal beam across a decorative window. If the window is 3 feet by 5 feet, then to the nearest hundredth, how long is the diagonal?
Answer:
12 square feet
Step-by-step explanation:
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Each week, Alfonso earns $85 for every shift he works at the theater and $15 for every dog-walking job. He uses the expression 85x + 15y to keep track of his earnings.
Part A: Identify the coefficients and variables in the expression. (3 points)
Part B: How many terms are in the expression, what are they, and how do you know? (4 points)
Part C: Which term in the expression shows the total earned from the dog-walking jobs? (3 points)
Please help with this question: A brick company guarantees to fill a contractor's order to within 5% accuracy. A contractor orders 1,500 bricks. Please write and solve an absolute-value equation to find the maximum and minimum number of bricks guaranteed.
A rectangular garden is fenced on all sides with 160 feet of fencing. The garden is 6 feet longer than it is wide. What is the area of the garden?
Use the graph below to answer the question that follows:
What trigonometric function represents the graph? (6 points)
Select one:
a. f(x) = −3 sin(x − pi over 2 )
b. f(x) = −3 cos(x − pi over 2 )
c. f(x) = 3 cos(x − pi over 2 )
d. f(x) = 3 sin(x − pi over 2 )
The trigonometric function which represents the graph is:
c) [tex]f(x)=-3\cos (x-\dfrac{\pi}{2})[/tex]
Step-by-step explanation:From the graph we may observe that when x=π/2 we have the value of the function f(x)= 3
Hence, we will check in which this point hold true:
a)
[tex]f(x)=-3\sin (x-\dfrac{\pi}{2})[/tex]
Now, when x=π/2 we have:
[tex]f(x)=-3\sin (\dfrac{\pi}{2}-\dfrac{\pi}{2})\\\\\\f(x)=-3\sin (0)\\\\\\f(x)=0\neq 3[/tex]
Hence, option: a is incorrect.
b)
[tex]f(x)=-3\cos (x-\dfrac{\pi}{2})[/tex]
Now, when x=π/2 we have:
[tex]f(x)=-3\cos (\dfrac{\pi}{2}-\dfrac{\pi}{2})\\\\\\f(x)=-3\cos (0)\\\\\\f(x)=-3\neq 3[/tex]
Hence, option: b is incorrect.
d)
[tex]f(x)=3\sin (x-\dfrac{\pi}{2})[/tex]
Now, when x=π/2 we have:
[tex]f(x)=3\sin (\dfrac{\pi}{2}-\dfrac{\pi}{2})\\\\\\f(x)=3\sin (0)\\\\\\f(x)=0\neq 3[/tex]
Hence, option: d is incorrect.
c)
[tex]f(x)=-3\cos (x-\dfrac{\pi}{2})[/tex]
Now, when x=π/2 we have:
[tex]f(x)=3\cos (\dfrac{\pi}{2}-\dfrac{\pi}{2})\\\\\\f(x)=3\cos (0)\\\\\\f(x)=3[/tex]
Similarly we will see that the value of this function matches all the points that on the graph.
Hence, option: c is correct.
1. A painter earns $15 per hour. What is the minimum number of hours he must work to earn at least $200? Write an inequality to represent this situation and solve. Show your work. (Will get brainiest if you show all work)
So you know that he earns $15 per hour so we can write that as 15h, h = # of hours worked
We also know he has to earn AT LEAST $200, so putting all this together we form the inequality(=< means less than or equal to): 15h =< 200
so now we have to solve for h (number of hours worked):
15h =< 200
(divide both sides by 15)
h =< 13 1/3
So, the painter must work a minimum of 13 and 1/3 hours to earn at least $200.
Hope this helps! :)
find the slope and y-intercept of the line that is parallel to y=-x-1 and passes through the point (5,-5)
Two angles form a linear pair. the measure of one angle is 26∘26∘ greater than the measure of the other angle. find the measure of each angle.
The measure of the smaller angle is 77 degrees, and the measure of the larger angle is 103 degrees.
Explanation:Let's represent the measure of the smaller angle as x degrees. Since the measure of one angle is 26 degrees greater than the other angle, the measure of the larger angle can be represented as x + 26 degrees.
According to the definition of a linear pair, the sum of the measures of two angles forming a linear pair is always 180 degrees. So we can write the equation:
x + (x + 26) = 180
Solving this equation, we get: 2x + 26 = 180
2x = 180 - 26
2x = 154
x = 154/2
x = 77
Therefore, the smaller angle measures 77 degrees and the larger angle measures 77 + 26 = 103 degrees.
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Michael is three times as old as Margaret, and in 6 years he will be twice as old as her. How old was Michael when Margaret was born?
Answer:
12 years old
Step-by-step explanation:
m = Michael
a = Margaret
m = 3a
m+6 = 2(a+6)
m+6 = 2a+12
Two equations, two unknowns, so we can use substitution.
3a+6 = 2a+12
a+6 = 12
a = 6
Plug it back in.
m = 3(6)
m = 18
When Michael was 18, Margaret was 6. So when she was born (basically when she was 0) Michael was 18-6 = 12.
Answer:
Michael was 12 years old when Margaret was born.
Step-by-step explanation:
Let Michael be x and Margaret be y.
x=3y
x+6 (years) = 2(6+y) --> x+6=12+2y --> x=6+2y
Now that we have x, substitute x=3y:
6+2y=3y --> y=6
Now we have y, substitute again with x=3(6) --> x=18
So, Michael, x, is 18 years old. Margaret, y, is 6 years old. But, to find how old Michael was when Margaret was born, do 18 (Michael's age)-6 (Margaret's age) to get 12. So, Michael was 12 years old when Margaret was born. Hope that helped, sorry if I missed something... :D
Long division 112 divided by 10 please show working out
If the correlation between variables is .60, what is the coefficient of alienation?
Given: f(x)=x²-3 and g(x)=x+1. What is the composite function gOf?
1. x²+2x-2
2. x²+2x-2
3. x²-2
For two given functions f(x) and g(x), the composite function
(g ° f)(x) is: g(f(x))
Here we will find that the correct option is the last one:
(g°f)(x) = x²-2
To get this, we know that:
g(x) = x + 1
f(x) = x² - 3
Then:
(g°f)(x) = g(f(x))
So here we just need to evaluate g(x) in f(x):
g(f(x)) = f(x) + 1 = ( x² - 3) + 1 = x² - 3 + 1 = x² - 2
Then the correct option is 3:
(g°f)(x) = x²-2
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1. How many solutions can a quadratic equation have and why does it vary? How would the corresponding graphs look like?
2. Describe the process of graphing a quadratic equation without using graphing technology.
3. Apply the projectile formula to a real-world situation.
Imagine that last night you saw the star betelgeuse just starting to rise on your eastern horizon at 7:15 pm. at 7:15 pm tonight, will betelgeuse be above, below, or exactly on your eastern horizon?
Final answer:
Betelgeuse will be either just above the horizon or at virtually the same position on the eastern horizon at 7:15 pm the next day, as stars like Betelgeuse rise in the east and set in the west, completing a rotation around the celestial sphere in about 24 hours.
Explanation:
The question pertains to the observation of the star Betelgeuse and its position relative to the horizon at a specific time from one day to the next. Since most stars rise in the east and set in the west, completing one full rotation around the celestial sphere in approximately 24 hours, we can infer that Betelgeuse will follow a similar path. However, due to Earth's rotation, any given star will appear to rise and set four minutes earlier each night, due to the Earth’s orbit around the Sun completing an extra degree each day. This might suggest that Betelgeuse would be slightly above the horizon at 7:15 pm the following night. Yet, the student should be aware that this four-minute difference can be negligible, and for practical observing purposes, Betelgeuse will be seen rising at virtually the same time, hence nearly at the same position on the horizon.
∠E and ∠F are vertical angles with m∠E=5x+10 and m∠F=7x−12 .
What is the value of x?
Answer: 11
Step-by-step explanation:
We are given that ∠E and ∠F are vertical angles with m∠E=5x+10 and m∠F=7x−12 .
We know that vertical angles are congruent, then their measures must be equal.
i.e. if ∠E and ∠F are vertical angles.
⇒ m∠E=m∠F
[tex]\Rightarrow\ 5x+10=7x-12[/tex] [Substitute the measures of ∠E and ∠F]
Subtract 5x from both sides , we get
[tex]10=2x-12[/tex]
Add 12 on both sides , we get
[tex]22=2x[/tex]
Divide both sides by 2 , we get
[tex]11=x[/tex] or x=11
Hence, the value of x= 11