The equivalent expression of the expression P (z ≥ 1.7) is,
⇒ 1 - P (z ≥ - 1.7)
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We have to given that;
The expression is,
⇒ P (z ≥ 1.7)
Now, By definition of Probability of z - score we get;
⇒ P (z ≥ 1.7) = 1 - P (z ≥ - 1.7)
Thus, The equivalent expression of the expression P (z ≥ 1.7) is,
⇒ 1 - P (z ≥ - 1.7)
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There are 160 children in a baseball league. 60% of those children are in middle school. How many children in the baseball league are in middle school?
The answer is 96 you’re welcome
Let me know the answer plz
Answer:
The correct answer option is B. [tex]1[/tex], [tex]\frac{1}{2}[/tex], [tex]\frac{1}{4}[/tex].
Step-by-step explanation:
We are given the following geometric sequence and we are to find its 8th term:
[tex]16, 8, 4, 2,...[/tex]
Here [tex]a_1=16[/tex] and common ratio [tex](r) = \frac{2}{4}=0.5[/tex].
The formula we will use to find the next three terms is:
nth term = [tex]a_1 \times r^{(n-1)}[/tex]
5th term = [tex]16 \times 0.5^{(5-1)} = 1[/tex]
6th term = [tex]16 \times 0.5^{(6-1)}[/tex] = [tex]\frac{1}{2}[/tex]
7th term = [tex]16 \times 0.5^{(7-1)}[/tex] = [tex]\frac{1}{4}[/tex]
Which linear function represents the line given by the point-slope equation y + 7 = –(x + 6)?
After distributing the -1, you will find
y+7= -x-6
Finally, isolate y to find your answer in the linear form of
y= -x-13
What is the value of x if line a is parallel to line b and is cut by a transversal?
Answer:
x=35
Step-by-step explanation:
The angles are alternate interior angles. Alternate interior angles are equal if the lines are parallel.
3x+16 = 5x-54
Subtract 3x from each side
3x -3x+16 = 5x-3x-54
16 = 2x-54
Add 54 to each side
16+54 = 2x-54+54
70 = 2x
Divide each side by 2
70/2 = 2x/2
35 =x
I need all the help I can get from you all
If 9(x - 9) = -11, then x = ?
-90
-2/9
70/9
108
Answer:
70/9
Step-by-step explanation:
multiply the parenthesis
add the constant together then divide
Answer:
70 / 9
Step-by-step explanation:
9(X - 9) = -11
9X - 81 = -11
9X = -11 + 81
9X = 70
X = 70 / 9
Lisa has an online jewelry shop where she sells earrings and necklaces. SHe sells earrings for $30 and necklaces for $40. It takes half an hour to make a pair of earrings and 1 hour to make a necklace. Lisa only has 10 hours a week to make jewelry. In addition, she only has enough materials to make 15 total jewelry items per week. She makes a profit of $15 on each pair of earrings and $20 on each necklace. How many pairs of earrings and necklaces should Lisa make each week in order to maximize her profit, assuming she sells all her jewelry?
Answer:
10 pairs of earrings and 5 necklaces (the maximum profit will be $250)
Step-by-step explanation:
Let x be the number of earrings and y be the number of necklaces Lisa makes.
1. Lisa only has enough materials to make 15 total jewelry items per week, then
[tex]x+y\le 15.[/tex]
2. It takes half an hour to make a pair of earrings, so it takes her [tex]\dfrac{1}{2}x[/tex] hours to make x earrings. It takes her 1 hour to make a necklace, so it takes her y hours to make y necklaces. Lisa only has 10 hours a week to make jewelry, thus
[tex]\dfrac{x}{2}+y\le 10[/tex]
3. Lisa makes a profit of $15 on each pair of earrings and $20 on each necklace. In total her profit is
[tex]P=15x+20y.[/tex]
You have to find the maximum value of the function [tex]P=15x+20y[/tex] with respect to inequalities
[tex]x+y\le 15\\ \\\dfrac{x}{2}+y\le 10[/tex]
Draw the solution set on the coordinate plane (see attached diagram). The maximum value of the efunction P is at point (10,5) and is
[tex]P=15\cdot 10+20\cdot 5=150+100=\$250[/tex]
Blake and Ned work for home remodeling business they are putting the final touches on a home they renovated. working alone Blake and paint one room in nine hours, Ned can paint the same room in six hours. how long will it take them to paint the room if they work together
Answer:
3.6 hours
Step-by-step explanation:
Blake can do work in hours = 9
Blake can do a part of work in 1 hour = [tex]\frac{1}{9}[/tex]
Ned can paint the same room in six hours.
Ned can do a part of work in 1 hour = [tex]\frac{1}{6}[/tex]
They can do a part of work together in 1 hour = [tex]\frac{1}{9}+\frac{1}{6}[/tex]
= [tex]\frac{5}{18}[/tex]
Now they can do [tex]\frac{5}{18}[/tex] part of work in hour = 1
So, they can do whole work in hours = [tex]\frac{1}{\frac{5}{18}}[/tex]
= [tex]3.6[/tex]
Hence it will take 3.6 hours to paint the room if they work together.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Five times the sum of the digits of a two-digit number is 13 less than the original number. If you reverse the digits in the two-digit number, four times the sum of its two digits is 21 less than the reversed two-digit number. (Hint: You can use variables to represent the digits of a number. If a two-digit number has the digit x in tens place and y in one’s place, the number will be 10x + y. Reversing the order of the digits will change their place value and the reversed number will 10y + x.) The difference of the original two-digit number and the number with reversed digits is .
Answer:
The difference of the original two-digit number and the number with reversed digits is 98 - 89 = 9
Step-by-step explanation:
Let the digit at unit(one's) place = y
Let the digit at ten's place = x
So, the two-digit number will be: 10x +y
According to given condition:
Five times the sum of the digits of a two-digit number is 13 less than the original number. This statement can be written as:
5(x +y) = (10x +y) - 13
If you reverse the digits in the two-digit number, four times the sum of its two digits is 21 less than the reversed two-digit number.
if digits are reserved the two digit will be 10y + x
4(x + y) = (10y + x) -21
So, we have 2 equations, solving these 2 equations we can find the 2 digit number.
5(x +y) = (10x +y) - 13
5x + 5y = 10x +y -13
Rearranging:
5x -10x +5y -y = -13
-5x + 4y = -13 (eq1)
4(x + y) = (10y + x) -21
4x +4y = 10y +x =-21
4x -x +4y -10y = -21
3x -6y = -21 (eq2)
Solving:
Multiply eq 1 with 3 and eq 2 with 2
-15x + 12 y = -39
6x - 12y = -42
_______________
-9x = -81
x = -81/-9
x = 9
Putting in eq(1)
-5x + 4y = -13
-5(9) +4y = -13
-45 + 4y = -13
4y = -13 + 45
4y = 32
y = 32/4
y = 8
So, y =8 and x = 9
The 2 digit number is:
10x + y = 10(9) + 8 = 90+8 = 98
The reversed 2 digit number is:
10y + x = 10(8) + 9 = 80+9 = 89
The difference of the original two-digit number and the number with reversed digits is 98 - 89 = 9
Solve 8x-5>or=27
Epic
Epic
Epic
Epic
Epic
Gamer momeent
For this case we must solve the following inequality:
[tex]8x-5 \geq27[/tex]
We add 5 to both sides of the inequality:
[tex]8x\geq27 + 5\\8x\geq32[/tex]
DIviding between 8 on both sides of the equation:
[tex]x \geq \frac {32} {8}\\x \geq4[/tex]
Thus, the solution is given by all the numbers greater than or equal to 4
Answer:
[tex]x \geq4[/tex]
Answer: [tex]x\geq4[/tex]
Step-by-step explanation:
Given the inequality [tex]8x-5\geq27[/tex], you need to solve for the variable "x".
You must follow these steps to solve for the variable "x":
- First, you need to add 5 to both sides of the inequality. Then:
[tex]8x-5+(5)\geq27+(5)\\\\8x\geq32[/tex]
- And finally, you need to divide both sides of the inequality by 8.
Therefore, you get:
[tex]\frac{8x}{8}\geq\frac{32}{8}\\\\x\geq4[/tex]
Which expression is equivalent to log w (x^2 -6)^4/ 3 sqrt x^2+8?
Answer:
C [tex]4\log_w(x^2-6)-\dfrac{1}{3}\log_w(x^2+8)[/tex]
Step-by-step explanation:
First use the property of logarithms
[tex]\log _ab-\log_ac=\log_a\dfrac{b}{c}.[/tex]
For the given expression you get
[tex]\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}[/tex]
Now use property of logarithms
[tex]\log_ab^k=k\log_ab.[/tex]
For your simplified expression, you get
[tex]\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=4\log_w(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).[/tex]
Answer: C
Step-by-step explanation:
PLEASE HELP ASAP!!!
The number of bacteria in a petri dish increases according to the function
y = 1000(3.7^x), where x is the number of hours. How many bacteria will
there be after 3 hours?
OA) 3700
OB) 35,650
OC) 50,653
OD) 63,505
Answer:
C) 50,653
Step-by-step explanation:
y = 1000(3.7)^x
After 3 hours x=3
y = 1000(3.7)^3
y = 1000(50.653)
y =50653
Answer: OPTION C
Step-by-step explanation:
You know that in the function [tex]y = 1000(3.7^x)[/tex] the variable "y" is the number of bacterias in a petri dish and the variable "x" is the number of hours.
Then, to answer the question "How many bacteria will there be after 3 hours?", you need to substitute [tex]x=3[/tex] into the function.
Therefore, the number of baterias after 3 hours will be:
[tex]y = 1000(3.7^3)[/tex]
[tex]y = 1000(50.653)[/tex]
[tex]y = 50,653[/tex]
This matches with the option C.
A container in the shape of a cone has a height of 13 centimeters and a diameter of 8 centimeters. Find the volume of the container to the nearest tenth of a centimeter. Use 3.14 for pi
if its diameter is 8 cm, then its radius is half that, or 4 cm.
[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=13 \end{cases}\implies V=\cfrac{\pi (4)^2(13)}{2} \\\\\\ V=104\pi \implies \stackrel{\pi =3.14}{V=326.7}[/tex]
What probability of Sammy choosing a red or yellow
Answer:
D.)1/8Step-by-step explanation:
the ishango bone eas found 20000years ago in the congo. why do archaeologist bellieved that the scratxhes on this bine was from people conting
Final answer:
The Ishango bone, found in the Congo with scratches believed to represent counting, shows evidence of prehistoric mathematical activity 20,000 years ago. It suggests early numerical understanding and supports the theory that Stone Age humans engaged in proto-mathematics.
Explanation:
The Ishango bone is a significant archaeological find believed by many archaeologists to be evidence of prehistoric mathematical activity. Found 20,000 years ago in what is now the Democratic Republic of Congo, the bone has a series of noticeable scratches that many scholars interpret as a form of counting. The precise nature of these markings is still the subject of debate, but the prevailing theory is that they were used for arithmetic operations, such as keeping track of numbers or simple calculations.
The archaeological context of the Ishango bone, being from the Stone Age, highlights the early presence of numerical comprehension, which could suggest that the humans of that era had some sense of numbers and possibly even a form of proto-mathematics. This idea is reinforced not just by the Ishango bone, but also by the evidence from various archaeological sites across Africa, where other mathematical tools and representations, such as carved stones with depictions of animal figures, which date back tens of thousands of years, have been found.
The discovery of the Ishango bone adds to a growing body of evidence that early humans had the ability to count and perform simple mathematical operations long before the establishment of formal systems of writing or the development of modern number systems. Such artifacts are invaluable for understanding the cognitive abilities of our early ancestors and the origins of mathematical practices.
Can someone help me with this
Answer:
Yes
Step-by-step explanation:
Try the points and see:
(x, y) = (-1, 3) . . . . x + y = -1 + 3 = 2 . . . . yes
(x, y) = (3, -1) . . . . x + y = 3 + (-1) = 2 . . . yes
The remaining points lie on the line connecting these points, so they, too will be on the graph of that line.
Helppp simplify (3^-2)^4
For this case we must simplify the following expression:
[tex](3 ^ {-2}) ^ 4[/tex]
By definition of power properties we have to:[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
So, rewriting the expression we have:
[tex](\frac {1} {3 ^ 2}) ^ 4 = \frac {1 ^ 4} {(3 ^ 2) ^ 4} = \frac {1} {(3 ^ 2) ^ 4}[/tex]
By definition of power properties we have:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So:
[tex]\frac {1} {(3 ^ 2) ^ 4} = \frac {1} {3 ^ 8}[/tex]
Answer:
Option D
A triangle with point (8, 10) undergoes a dilation with a scale factor of 1/2. What are the new coordinates of the point?
Answer:
(4, 5)
Step-by-step explanation:
Answer:
New x-coordinate: 4
New y-coordinate: 5
New point: (4,5)
Step-by-step explanation:
You know that the coordinates of a point of this triangle are the following:
[tex]x_1=8\\y_1=10[/tex]
And you know that it is dilated with a scale factor of [tex]\frac{1}{2}[/tex], then, to find the new coordinates of the point, you need to multiply the original coordinates by the scale factor:
New x-coordinate:
[tex]x_2=\frac{1}{2}x_1[/tex]
[tex]x_2=\frac{1}{2}(8)[/tex]
[tex]x_2=4[/tex]
New y-coordinate:
[tex]y_2=\frac{1}{2}y_1[/tex]
[tex]y_2=\frac{1}{2}(10)[/tex]
[tex]y_2=5[/tex]
The new point is (4,5)
Cari owns a horse farm and a horse trailer that can transport up to 8,000 pounds of livestock and tack. She travels with 5 horses whose combined weight is 6,240 pounds. Let t represent the average weight of tack per horse. Which of the following inequalities could be used to determine the weight of tack Cari can allow for each horse?
Answer:
5(1248 lb/horse + t lb) ≤ 8000 lb
Step-by-step explanation:
One way to do this is to find the average weight of the 5 horses:
It is:
6,240 lb
---------------- = 1248 lb/horse
5 horses
and to this, for each horse, we must add t lbs tack.
Thus, 5(1248 lb/horse + t lb) ≤ 8000 lb
would be an appropriate inequality.
Please note that your question mentions "the following inequalities;" that means you are expected to share them! Please do so next time. Thanks.
What statement helps answer this question
I would say option A best proves it is a parallelogram.
Quinn and Derek bought office supplies together. Quinn bought 10 packs of paper and 12 boxes of pens for a total cost of $33. Derek bought 15 packs of paper and 7 boxes of pens for a total of $27.50. How much was one pack of paper? How much was one box of pens?
Answer:
The cost of one pack of paper was $0.90 and the cost of one box of pens was $2.00
Step-by-step explanation:
Let
x----> the cost of one pack of paper
y---> the cost of one box of pens
we know that
10x+12y=33 ----> equation A
15x+7y=27.50 ---> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point (0.9,2)
see the attached figure
Therefore
The cost of one pack of paper was $0.90
The cost of one box of pens was $2.00
Answer:
pens = $2
paper = .9
Step-by-step explanation:
p = price of a pack of paper
n = price of a box of pens
10p + 12n = 33
15p + 7n = 27.50
Multiply the first equation by 3
3(10p + 12n )= 33*3
30p +36n = 99
Multiply the second equation by -2
-2(15p + 7n) = 27.50*-2
-30p -14n = -55
Add the 2 modified equations together
30p +36n = 99
-30p -14n = -55
--------------------
22n = 44
Divide each side by 22
22n/22 = 44/22
n =2
Each box of pens is $2
Now we can find the price of the paper
10p + 12n = 33
10p +12(2) = 33
10p +24 =33
Subtract 24 from each side
10p+24-24=33-24
10p = 9
Divide by 10
10p/10 =9/10
p = .9
helped needed asap 20 points!! and brainliest
ANSWER
1. No solution
2. 4 and 6
3. 81
EXPLANATION
1. The given quadratic equation is
[tex] {x}^{2} + 1 = 0[/tex]
This implies that:
[tex] {x}^{2} = - 1[/tex]
There is no real number whose square is negative one.
This quadratic equation has no solution.
2. The given quadratic equation is
[tex] {x}^{2} - 10x + 24 = 0[/tex]
We split the middle term with -6,-4 because their product is 24 and their sum is -10
[tex]{x}^{2} - 6x - 4x+ 24 = 0[/tex]
We factor by grouping
[tex]{x}(x - 6)- 4(x - 6)= 0[/tex]
[tex](x - 6)(x - 4)= 0[/tex]
We have x=4 and x=6.
3. The given quadratic equation is
[tex] {x}^{2} - 18x = 7[/tex]
We the square of half the coefficient of x to both sides of the equation.
[tex]( - \frac{18}{2} )^{2} = ( { - 9)}^{2} = 81[/tex]
The correct choice is C.
Determine the relationship between the two vecors
Answer:
Addition of two vectors Will make an resultant vector or a third vectors
Step-by-step explanation:
When two vectors represents in both magnitude and direction as two sides of triangle then resultant will represent as both as third side of triangle but in opposite order
Two different antibiotics can be used to treat an infection. Treatment with antibiotic 1 is known to be successful 80% of the time. This treatment costs $80. Antibiotic 2 is successful 90% of the time and costs $100. The two treatment plans are: Plan A: Treat with antibiotic 1. If not effective, treat with antibiotic 2. Plan B: Treat with antibiotic 2. If not effective, treat with antibiotic 1. Based on the data provided, what is the expected cost per patient under plan B?
A. $100
B. $80
C. $180
D. $108
Answer: Option D
D. $108
Step-by-step explanation:
We must calculate the expected cost per patient to use treatment method B.
The expected cost for a discrete random variable x is:
[tex]C = \sum x_i * P (x_i)[/tex]
Where [tex]x_i[/tex] is the cost associated with the probability [tex]P(x_i)[/tex]
In this case, the random variable x is represented by the cost of each treatment.
For treatment B there is a possibility that antibiotic 2 works, in that case the cost x would be $ 100 and [tex]P (x) = 0.9[/tex]
There is also the possibility that it does not work, in this case the cost x would be $180 and the probability [tex]P (x) = 0.10[/tex]
The expected cost is:
[tex]C =\$100*0.9 + \$180*0.1\\\\C = \$108[/tex]
In a jar, the numbers of white, black and red marbles are in ratio of 5:11:8. If the total number of marbles is 144, then how many red marbles are there?
Answer:48 red marbles
Step-by-step explanation:
144÷24= 6
6*5= 30 white
6*11= 66 black
6*8= 48 red
Answer: The number of red marbles in the jar is 48.
Step-by-step explanation: Given that the number of white, black and red marbles in a jar are in the ratio 5 : 11 : 18. And the total number of marbles in the jar is 144.
We are to find the number of red marbles in the jar.
Let, 5x, 11x and 8x be the number of white, black and red marbles in the jar.
Then, according to the given information, we have
[tex]5x+11x+8x=144\\\\\Rightarrow 24x=144\\\\\Rightarrow x=6.[/tex]
Therefore, the number of red marbles will be
[tex]8x=8\times6=48.[/tex]
Thus, there are 48 red marbles in the jar.
what is the volume of a triangular pyramid that is 10 inches tall and has a base area of 9 square inches please help
Answer:30
Step-by-step explanation: V=1/3 Bh, 9x10=90 divide that by 3 for 30
The volume of a triangular pyramid that is 10 inches tall and has a base area of 9 square inches is 30 cubics in.
What is a triangular pyramid?Take a triangle. This is a base.
Now take 3 triangles such that each of them is connected to the one-one side of the first triangle and when they're taken together, they form a closed object, called a triangular pyramid.
The volume of a triangular pyramid that is 10 inches tall and has a base area of 9 square inches
The volume of a triangular pyramid
V = 1/3 x B x h,
V = 1/3 x 9 x 10
V = 3 x 10
V = 30
Hence, the volume will be 30 cubics in.
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What is the solution to the equation x + 5.7 = 6.1?
x = 0.4
x = 0.6
x = 1.4
x = 11.8
The solution is X=0.4
The answer is the first one
Consider the graph of Miriam's bike ride to answer the
questions,
How many hours did Miriam stop to rest?
How many hours did it take Miriam to bike the initial 8
miles?
Answer:
1) 45 minutes or 0.75 hours
2) 45 minutes or 0.75 hours
Step-by-step explanation:
We are given the graph that shows Miriam's bike ride.
The x-axis represents the time (in minutes) and the y-axis represents the distance traveled in miles.
1) How many hours did Miriam stop to rest?
The graphs stays the same from 45 minutes to 90 minutes, where he took the rest. No distance covered in that time.
Rest time = 90 minutes - 45 minutes = 45 minutes
He took rest for 45 minutes.
In hours, it is 45/60 = 0.75 hours
2) How many hours did it take Miriam to bike the initial 8 miles.
Look at the graph, the graph reached 8 miles when the time was 45 minutes.
It took 45 minutest to reach 8 miles initially.
In hours, it is 45/60 = 0.75 hours
which is the rate of change of the function described in the table?
12/5
5
25/2
25
The rate of change of the function can be determined by finding the slope of the function at different points in the table.
Explanation:The rate of change of a function can be determined by finding the slope of the function at different points. In this case, we can use the values provided in the table to find the rate of change. The rate of change is equal to the difference in the y-values divided by the difference in the x-values.
Let's take the first two points in the table as an example. The first point is (12/5, 5) and the second point is (5, 25/2). The difference in the y-values is 25/2 - 5 = 15/2, and the difference in the x-values is 5 - 12/5 = 23/5. Therefore, the rate of change is (15/2) / (23/5) = 15/2 * 5/23 = 75/46. So, the rate of change of the function for these two points is 75/46.
In the coordinate plane, three vertices of rectangle HDK are H(0, 0), (0, d), and Kle, 0). What are the coordinates of point J?
Answer:
K = (e, d)
Step-by-step explanation:
We are given the coordinates of three vertices of a rectangle and we are to find the coordinates of the fourth point J.
H (0, 0)
I (0, d)
K (e, 0)
J = ?
We can find this using the following formula:
K = H + (I - H) + (K - H)
K = H + I - H + K - H
K = I + K - H
Substituting the given values in it to get:
K = [tex](0, d) + (e, 0) - (0, 0)[/tex]
K = [tex](0+e-0, d+0-0)[/tex]
K = (e, d)
The triangles shown below must be congruent.
Answer:
A
Step-by-step explanation:
If the corresponding parts of the triangles are congruent then the triangles are congruent.
Here there are 2 corresponding congruent angles, that is 51° and 80°
The non- included corresponding sides are congruent both 10
Then by AAS postulate the triangles are congruent- True
Answer:
True
Step-by-step explanation:
A pex