Answer:
z less-than negative 19 or z greater-than 11Step-by-step explanation:
Given the inequality [tex]|z+4|>15[/tex], we are to find the solution set of the inequality. Since the the function is an absolute value, this means that the function will be positive and negative.
For the positive value of the function;
[tex]z+4>15\\\\subtract\ 4\ from \ both \ sides\\z+4-4 > 15 -4\\\\z>11[/tex]
For the negative value of the function we have;
[tex]-(z+4) > 15\\\\-z-4> 15\\add\ 4 \ to\ both \ sides\\\\-z-4+4> 15+4\\\\-z> 19\\\\[/tex]
Multiplying both sides of the inequality by -1 will change the sense of the inequality sign;'
[tex]-(-z)< -19\\\\z<-19[/tex]
Hence the solution sets are [tex]z> 11 \ and \ z< -19 \\[/tex] OR z less-than negative 19 or z greater-than 11
Answer:
z less-than negative 19 or z greater-than 11
Step-by-step explanation:
Let f(x)=x+8 and g(x)= x2-6x-7 find f(g2)
Answer:
-7.
Step-by-step explanation:
g(x) = x^2 - 6x - 7
g(2) = 2^2 - 6(2) - 7
= 4 - 12 - 7
= -8 - 7
= -15
f(x) = x + 8
f(-15) = (-15) + 8
= 8 - 15
= -7
Hope this helps!
A piece of buttered toast falls to the floor 17 times. The toast landed buttered side up 6 times. What is the probability that the toast lands buttered side down?
Step-by-step explanation:
Given that,
A piece of buttered toast falls to the floor 17 times. The toast landed buttered side up 6 times.
It means that the total number of outcomes are 17
We need to find the probability that the toast lands buttered side down. Favourable oucome is 17-6 = 11
So, probability is given by :
[tex]P(E)=\dfrac{\text{favourable outcomes}}{\text{total no of outcomes}}[/tex]
[tex]P(E)=\dfrac{11}{17}[/tex]
So, the probability that the toast lands buttered side down is 11/17.
Solve the following equation using the square root property.
9x2 + 10 = 5
Find the area of the shaded triangle below.
Answer:
A = 12 square units
Step-by-step explanation:
Area of a Triangle = base * height / 2
The triangle might look weird and doesn't look like it has a base, but if you look at the left side you see there is a straight line which means there is a base, so we flip the picture until we see that the flat line on the bottom or the base.
The base is 4 units.
To find the height, we don't need a straight line, we just need to see how the tall the triangle is, to do that you must start from the lowest point and count up to the highest point.
You now get 6 units.
A = bh/2
A = 4*6/2
A = 24/2
A = 12 square units
The distance between two cities on a map is 4 centimeters. If the scale is 0.5 cm:1 km, how many kilometers apart are the actual cities?
Answer:
8 km
Step-by-step explanation:
1 km
4 cm x -------- = 8 km
0.5 cm
The actual cities are 8 km apart from each other at the scale 0.5 cm = 1 km.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
The distance between two cities on a map = 4 centimeters.
Also, the scale
0.5 cm = 1 km
To find actual distance between cities, use ratio properly,
0.5 cm = 1 km
1 cm = 2 km
4 cm = 8 km
The distance between the actual cities is 8 km.
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what is sum of all palindromic numbers from 1 to 100
Answer:
540
Step-by-step explanation:
0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99
Answer:
540
Step-by-step explanation:
Hey there!
Well we need to first find all the palindromic numbers,
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99
Add
= 540
Hope this helps :)
solve for x: 5x+3+8x-4=90
Answer:
[tex]x = 7[/tex]
Step-by-step explanation:
We can solve the equation [tex]5x+3+8x-4=90[/tex] by isolating the variable x on one side. To do this, we must simplify the equation.
[tex]5x+3+8x-4=90[/tex]
Combine like terms:
[tex]13x - 1 = 90[/tex]
Add 1 to both sides:
[tex]13x = 91[/tex]
Divide both sides by 13:
[tex]x = 7[/tex]
Hope this helped!
Answer:
x = 7
Step-by-step exxplanation:
5x + 3 + 8x - 4 = 90
5x + 8x = 90 - 3 + 4
13x = 91
x = 91/13
x = 7
probe:
5*7 + 3 + 8*7 - 4 = 90
35 + 3 + 56 - 4 = 90
Which of the following is the solution set of the given equation? (x - 3) - 2(x + 6) = -5 a) {-4} b) {8} c) {-10}
Answer:
x = -10
Step-by-step explanation:
(x - 3) - 2(x + 6) = -5
Distribute
x-3 -2x-12 = -5
Combine like terms
-x -15 = -5
Add 15 to each side
-x-15+15 = -5+15
-x=10
Multiply each side by -1
x= -10
Answer:
c
Step-by-step explanation:
Determine which is the appropriate approach for conducting a hypothesis test. Claim: The mean RDA of sodium is 2400mg. Sample data: n150, 3400, s550. The sample data appear to come from a normally distributed population.
Answer:
Use the student t distribution
Step-by-step explanation:
Here is the formula
t = (x - u) ÷(s/√N)
From the information we have in the question:
n = 150
s = 550
x = 3400
u = mean = 2400
= 3400 - 2400÷ 500/√150
= 1000/44.9
= 22.27
At 0.05 significance level, df = 149 so t tabulated will be 1.65.
We cannot use normal distribution since we do not have population standard deviationWe cannot use normal distribution since we do not have population standard deviationChisquare cannot be used since we are not testing for population varianceWe cannot use normal distribution since we do not have population standard deviationChisquare cannot be used since we are not testing for population varianceThe parametric or bootstrap method cannot be used either.Which equation is equivalent to StartRoot x EndRoot + 11 = 15?
Answer:
D [tex]\sqrt{x} +11=15[/tex]
Step-by-step explanation:
Edge 2020
For the given expression √x + 11 = 15 the value of x will be equal to 16.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression √x + 11 =15. The expression will be solved as below,
√x + 11 =15
√x = 15 - 11
√x = 4
Squaring on both sides of the equation,
x = 4²
x = 16
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In a survey of 15000 students of different schools, 40% of them were found to have tuition before the see examination. Among them 50% studied only mathematics ,30% only science and 10% studied others subject. how many student studied mathematics as well as science.
Answer: 600 students.
Step-by-step explanation:
Ok, we start with 15,000 students.
40% of them had tuition, so the actual number of them that had tuition is:
15,000*0.40 = 6,000.
Now we want to find the number of students that studied math and science.
50% only studied math,
30% only studied science
10% studied other subjects.
So 50% + 30% + 10% did NOT studied both math and science
90% is the percentage that did not study math and mathematics as well as science, then the other 10% did.
Then, out of the 6,000 students that had tuition, 10% studied math and science, the total number is:
6,000*0.10 = 600
nick cut a circular cookie into 5 equal slices. what is the angle measure of each slice?
Using concepts of circles, it is found that the angle measure of each slice is of 72º.
--------------------------------------------
The cookies have circular formats.A complete circle, which is the format of a cookie, has an angular measure of 360º.If it is divided into a number n of equal slices, the angles will be 360 divided by n.--------------------------------------------
5 equal slices, thus:
[tex]\frac{360}{5} = 72[/tex]
The angle measure of each slice is of 72º.
A similar problem is given at https://brainly.com/question/16746988
Which expression is equivaleny to 0.7 + p + 0.86p?
A.1 + 1.56p
B.p + 1.56
C.2.56p
D. -0.84p
Answer:
None of the above.
1.86p + 0.7
Step-by-step explanation:
Step 1: Write expression
0.7 + p + 0.86p
Step 2: Combine like terms
0.7 + 1.86p
None of those answer choices are correct unless you wrote the problem incorrectly.
simplify the following expression by combining like terms 2x+7x^2-5x+8x^2
Answer:15x^2-3x
Step-by-step explanation:
Factor the expression completely. 6×3- 4×2 – 16x A. 0 B. 2x(3×2 – 2x – 8) C. 2x(3x + 4)(x – 2) D. 4x(2x + 1)(x – 4) E. 2x(2×2 + 7x – 4) ill give brainliest
Answer:
The answer is option CStep-by-step explanation:
6x³ - 4x² - 16x
To factorize the expression first factor out the GCF out
The GCF in the expression is 2x
That's
2x( 3x² - 2x - 8)
Next Factorize the terms in the bracket
To factorize write - 2x as a difference
that's
2x( 3x² + 4x - 6x - 8)
Factor out x from the expression
2x [ x( 3x + 4) - 6x - 8 ]
Next factor out - 2 from the expression
2x [ x ( 3x + 4) - 2( 3x + 4) ]
Factor out 3x + 4 from the expression
We have the final answer as
2x( 3x + 4)( x - 2)Hope this helps you
PLZ answer quick i will give brainliest if right no explanation needed Joe is responsible for reserving hotel rooms for a company trip. His company changes plans and increases how many people are going on the trip, so they need at least 50 total rooms. Joe had already reserved and paid for 161616 rooms, so he needs to reserve additional rooms. He can only reserve rooms in blocks, and each block contains 8 rooms and costs $900. Let B represent the number of additional blocks that Joe reserves. 1) Which inequality describes this scenario? Choose 1 answer: a: 16+8B≤50 b: 16+8B≥50 c: 16+B≤50 d: 16+B≥50 2) What is the least amount of additional money Joe can spend to get the rooms they need?
Answer:
16 + 8b ≥ 50
4500
Step-by-step explanation:
He needs at least 50 rooms and has already reserved 16
They are in groups of 8
16 + 8b ≥ 50
Subtract 16 from each side
16+8b-16 ≥ 50 -16
8b≥ 34
Divide by 6
8b/8 ≥ 34/8
b≥ 4.25
We need to round up since we need at least 50
b = 5 since we want the least amount of rooms
Each block is 900
5*900 = 4500 more that he will have to spend
Suppose that the function g is defined, for all real numbers, as follows.
find g(-5) g(1) g(4)
=================================================
Explanation:
The piecewise function shows that we have two cases. Either x = 1 or [tex]x \ne 1[/tex].
If x = 1, then g(x) = 3 as shown in the bottom row. This is why g(1) = 3.
If [tex]x \ne 1[/tex], then g(x) = (1/4)x^2-4
Plug x = -5 into this second definition
g(x) = (1/4)x^2-4
g(-5) = (1/4)(-5)^2-4
g(-5) = (1/4)(25)-4
g(-5) = 25/4 - 4
g(-5) = 25/4 - 16/4
g(-5) = 9/4
Repeat for x = 4
g(x) = (1/4)x^2-4
g(4) = (1/4)(4)^2-4
g(4) = (1/4)(16)-4
g(4) = 4-4
g(4) = 0
The value of the function at x = -5, x = 1, and x = 4 will be 2.25, 3, and 0, respectively.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The functions are given below.
g(x) = (1/4)x² - 4, x ≠ 1
g(x) = 3, x = 1
The value of the function at x = -5 will be given as,
g(-5) = (1/4)(-5)² - 4
g(-5) = 25 / 4 - 4
g(-5) = 6.25 - 4
g(-5) = 2.25
The value of the function at x = 4 will be given as,
g(4) = (1/4)(4)² - 4
g(4) = 16 / 4 - 4
g(4) = 4 - 4
g(4) = 0
The value of the function at x = 1 will be given as,
g(1) = 3
The value of the function at x = -5, x = 1, and x = 4 will be 2.25, 3, and 0, respectively.
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Gina, Sam, and Robby all rented movies from the same video store. They each rented some dramas, comedies, and documentaries. Gina rented 11 movies total. Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. He rented 27 movies total. If Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, how many movies of each type did Gina rent?
Hi there! :)
Answer:
Gina rented 3 dramas, 5 comedies, and 3 documentaries.
Step-by-step explanation:
To solve, we will need to set up a system of equations:
Let x = # of dramas, y = # of comedies, and z = # of documentaries:
Write equations to represent each person:
Gina:
x + y + z = 11
Sam:
2x + 3y + 2z = 27
Robby:
x + 2y + 2z = 19
Write the system:
x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
Begin by subtracting the third equation from the second:
2x + 3y + 2z = 27
x + 2y + 2z = 19
-----------------------
x + y = 8
If x + y = 8, plug this into the first equation:
(8) + z = 11
z = 11 - 8
z = 3
We found the # of documentaries Gina rented, now we must solve for the other variables:
Subtract the top equation from the third. Substitute in the value of z we solved for:
x + 2y + 2(3) = 19
x + y + (3) = 11
-------------------------
y + 3 = 8
y = 5
Substitute in the values for y and z to solve for x:
x + 5 + 3 = 11
x + 8 = 11
x = 11 - 8
x = 3.
Therefore, Gina rented 3 dramas, 5 comedies, and 3 documentaries.
Answer:
B- x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
Step-by-step explanation:
I took the quiz
Dante is baking two different recipes, cookies and brownies. The cookie recipe requires 1.5 cups of sugar, and the brownie recipe requires 1.25 cups of sugar. Write an addition equation to represent the total amount of sugar Dante needs.
Answer: 1.5 cups of sugar + 1.25 cups of sugar = 2.75 cups of sugar for both recipes.
Step-by-step explanation:
Dante is baking two recipes.
A cookie recipe, that needs 1.5 cups of sugar.
A brownie recipe, that needs 1.25 cups of sugar.
So the total sugar that he needs is:
The sugar for the cookies + the sugar for the brownies:
The equation is:
1.5 cups of sugar + 1.25 cups of sugar = 2.75 cups of sugar.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A sampling distribution is normal only if the population is normal. Choose the correct answer below. A. The statement is false. A sampling distribution is normal only if n30. B. The statement is false. A sampling distribution is normal if either n30 or the population is normal. C. The statement is true. D. The statement is false. A sampling distribution is never normal.
The statement is false. A sampling distribution is normal if either n > 30 or the population is normal.
==========================================
Explanation:
If the underlying population is normally distributed, then so is the sample distribution (such as the distribution of sample means, aka xbar distribution).
Even if the population isn't normally distributed, the xbar distribution is approximately normal if n > 30 due to the central limit theorem. Some textbooks may use a higher value than 30, but after some threshold is met is when the xbar distribution is effectively "normal".
Choice A is close, but is missing the part about the population being normal. If we know the population is normal, then n > 30 doesn't have to be required.
One model of the length LACL of a person's anterior cruciate ligament, or ACL, relates it to the person's height h with the linear function LACL=0.04606h−(41.29 mm) This relationship does not change significantly with age, gender, or weight. If a basketball player has a height of 2.13 m, approximately how long is his ACL?
Answer:
The [tex]L_{ACL}[/tex] of the player is [tex]L_{ACL} = 56.82 \ mm[/tex]
Step-by-step explanation:
From the question we are told that
The relationship between the length [tex]L_{ACL}[/tex] to the height is
[tex]L_{ACL} = 0.04606h - (41.29 \ mm)[/tex]
The height of the basketball player is [tex]h = 2.13 \ m = 2130 \ mm[/tex]
Substituting the value of height of the basket ball player in to the model we have the [tex]L_{ACL}[/tex] of the player is
[tex]L_{ACL} = 0.04606 (2130) - (41.29 ) \ mm[/tex]
[tex]L_{ACL} = 56.82 \ mm[/tex]
What is the slope of the line shown below?
A. -3/2
B. 3/2
C. 2/3
D. -2/3
Answer:
2/3
Step-by-step explanation:
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= (1- -7)/(9 - -3)
= ( 1+7)/( 9+3)
= 8/12
Simplifying
= 2/3
Answer:
C. 2/3
Step-by-step explanation:
You can use the equation: [tex]y_{2} - y_{1}/x_{2} - x_{1}[/tex] to find the slope.
y2 is equal to the y coordinate of the second point: 1
y1 is equal to the y coordinate of the first point: -7
x2 is equal to the x coordinate of the second point: 9
x1 is equal to the x coordinate of the first point: -3
So if you plug these values into the equation, you will get:
1 - (-7)/ 9- (-3)
= 1 + 7/ 9 + 3
= 8/12
= 2/3
-50 POINTS- (5/5) Which scatter plot represents the following data?
Answer:
B is plotted correctly
Step-by-step explanation:
A point (1,2) is plotted at (1,3)
B is plotted correctly
C point (1,2) is plotted at (1,3)
D point (1,2) is plotted at (1,3)
Answer:
B.
Step-by-step explanation:
According to the table, there is a point at (0, 5), and a point at (1, 2).
A: The scatterplot has a point at (0, 5), but a point at (1, 3).
B: The scatterplot has points at (0, 5) and (1, 2).
C: The scatterplot has a point at (0, 5), but a point at (1, 3).
D: The scatterplot has a point at (0, 5), but a point at (1, 3).
Hope this helps!
Variable g is 8 more than variable w. Variable g is also 2 less than w. Which pair of equations best models the relationship between g and w? g = 8w g = w + 2 w = g + 8 w = g − 2 w = 8g w = g + 2 g = w + 8 g = w − 2
Answer: g = w + 8 g=w-2
Step-by-step explanation:
We could represent the word phrases by the equations.
g = w + 8
g = w - 2
Answer:
g = w + 8
g = w - 2
Step-by-step explanation:
Assuming that g and w exists, then we can show the relation as described:
"Variable g is 8 more than variable w."
g = w + 8
"Variable g is also 2 less than w."
g = w - 2
These are the two equations of the described relationship between g and w.
Note that g could not actually exist in the real number system:
g = w + 8
g = w - 2
w + 8 = w - 2
w - w = -2 - 8
0 != -10
This is impossible within the real number system.
Cheers.
How many times does 1/4 go into 3/8
Answer:
3/2
Step-by-step explanation:
3/8 ÷ 1/4
Copy dot flip
3/8 * 4/1
12/8
Divide top and bottom by 4
3/2
Caleb made 6 quarts of trail mix for his camping trip. Each week,he ate 4 pints of the trail mix. How many weeks did Caleb have trail mix?
Sry if this is too much
Answer:
3 weeks
Step-by-step explanation:
6 quarts = 12 pints
12 divided by 3 = 4
Step-by-step explanation:
1 quart = 2 pints
6 quarts = 2 x 6 = 12 pints
12 ÷ 4 = 3
He can have 3 weeks
8/2(2+2)
What is the answer?
Answer:
16
Step-by-step explanation:
[tex]\frac{8}{2} x (2+2) = \frac{8}{2} x 4 = \frac{8 x 4}{2} = \frac{32}{2} = 16[/tex]
Answer: 16
PEMDAS
P: Parenthesis
E: Exponents
M: Multipcaction
D: Divison
A: Addition
S: Subtraction
PEMDAS can be also known as Please Excuse My Dear Aunt Sally
P: (2+2)
E: N/A (There are no exponents)
M: 4×4
D: 8÷2
A: 2+2
S: N/A (There is nothing to subtract)
How did we get 4×4? We divided 8÷2 which got us 4. Then we added 2+2 and we also got 4. Then we multiplied 4×4 which got us 16. That's how 16 is our answer.
The MCAT is the admission exam that medical schools use as one of the criteria for accepting students. The exam is based on a scale of 0-45. The following data shows the MCAT scores for nine students.
32 36 29 31 30 35 34 26 30
The 35th percentile of this data set is:________
a. 31
b. 32
c. 31.5
d. 30
Answer:
d. 30
Step-by-step explanation:
The computation of the 35th percentile of this data set is shown below:
Before that first we have to series the number in ascending number
S. No Numbers
1 26
2 29
3 30
4 30
5 31
6 32
7 34
8 35
9 36
Now use the formula
Here n = 9
Percentile = 100
[tex]= \frac{35(9 + 1)}{100} \\\\[/tex]
= 3.5th
= 3th + 0.5 (4th - 3th)
= 3th + 0.5 (30 - 30)
= 3th + 0
= 30
8÷2(2+2)=?
I asked a few people some say it’s 1 and some say 16....
Answer:
16
Step-by-step explanation:
Follow the rules of PEMDAS
8÷2(2+2)
Parentheses
8÷2(4)
Exponents
we have none
Multiply and Divide from left to right
4(4)
16
Then Add and Subtract from left to right
Answer:
16
Step-by-step explanation:
In order to understand the answer to the problem, we need to know the correct order of operations, through the acronym PEMDAS
PEMDAS
P: Parentheses
E: Exponent
M: Multiply
D: Divide
A: Add
S: Subtract
First add everything in the parentheses to get 4
Then divide 8 by 2 to get 4
4 times 4 = 16
8/2= 4
2+2=4
4 x 4 = 16
A boutique wants to make at least $127 profit from purses this week. The boutique earns $7 profit from each purse. How many purses must be sold?
Answer:
19 purses
Step-by-step explanation:
Set up an inequality where x represents the number of purses:
127 [tex]\geq[/tex] 7x
Solve for x by dividing each side by 7:
18.14 [tex]\geq[/tex] x
Round up to 19 because purses have to be whole
So, 19 purses have to be sold.
