The normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution.
The usual normal distribution is then followed by the z variable. A value of the x variable's z variable, also known as the z-score of the x variable, indicates how many standard deviations from the mean it is.
The area under the normal distribution curve must be calculated that lies between
z=−1.56 and z=1.56
Using the standard normal table, the area is calculated as:
P(−1.56<z<1.56)
=P(z<1.56)−P(z<−1.56)
=P(z<1.56)−(1−P(z<1.56))
=0.9406−(1−0.9406)
=0.8812
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The complete question is
if z is a standard normal variable, find the probability. the probability that z lies between -1.56 and 1.56 is
A: What is the solution to b² = 196?
Answer:
b=14
Step-by-step explanation:
b^2=196
Square root both sides
b=14
Hopes this helps please mark brainliest
Answer:
14
Step-by-step explanation:
You're just looking for the square root of 196, and [tex]\sqrt{196} = 14[/tex]
140 is what percent
less than 160 ? PLSASE HELP
Answer:
The answer should be 12.5%
Please help me with the question in the picture
Answer:
7.5
Step-by-step explanation:
W -- X -- Y ----- Z
We are given that :
Y is the midpoint of WZ meaning that WY = YZX is the midpoint of WY meaning that WX = XY WY = 5Given this we want to find XZ
XZ consists of XY and YZ so we must find the length of the individual segments.
Finding YZ
Here, we know that YZ = WY as y is the midpoint of WZ. If WY = 5 then YZ also = 5
Finding XY
Given that WY = 5 and that X is a midpoint of WY we know that the segments WX and XY = WY and are congruent.
In other words we can say that 2XY = WY
==> WY = 5
2XY = 5
==> divide both sides by 2
XY = 2.5
Finding XZ
Again, XY + YZ = XZ
We have XY = 2.5 and YZ = 5
Hence, 2.5 + 5 = XZ
XZ = 7.5
Answer:
XZ = 7.5
Step-by-step explanation:
A drawing is sometimes very helpful.
Start by drawing a segment with endpoints W and Z.
+--------------------------------------------+
W Z
Y is the midpoint of WZ. Draw point Y in between W and Z and the same distance from both W and Z.
+---------------------+--------------------+
W Y Z
X is the midpoint of WY. Draw X between W and Y, and the same distance to W and Y.
+----------+----------+--------------------+
W X Y Z
Because of the midpoints, we know that:
WX = XY
WY = YZ
WY = 5
WX and XY are each half of WY, so WX = XY = 5/2 = 2.5
WY = YZ = 5
XZ = XY + YZ
XZ = 2.5 + 5
XZ = 7.5
Please answer this is due today
"In a fruit salad, there are 12 strawberries, 14 grapes, and 4 mangos. Find the ratio of mangos to grapes. Write the ratio using a colon in the simplest form"
Answer:
The ratio of mangos to grapes is 2:7.
Step-by-step explanation:
The original ratio of mangos to grapes would be 4:14. When it says mangos to grapes, it means mangos first, then grapes. If it said grapes to mangos, the grapes would go first. But, in this case the mangos go first. Now, we don't worry about the strawberries because it says to find the ratio of mangos to grapes, which is 4:14. Now, it says to simplify it to the simplest form. So, we can do this by dividing both numbers by the same number down as far as they can go as a whole number (a number without a decimal):
4 ÷ 2 = 2
14 ÷ 2 = 7
So, this is as far as we can go. So, our final answer is 2:7.
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Answer:
2:7
Step-by-step explanation:
4 mangos for every 14 grapes
the ratio right now is 4:14 this can be simplified by dividing by 2
4 divided by 2 = 2 ( 2 x 2 = 4 )
14 divided by 4 = 7 ( 7 x 2= 14)
Now the ratio is 2:7, or 2 mangos for every 7 grapes we know this is right because in order to use the amount the recipe calls for you need to double the answer
(adding separately is easier)
2+2 = 4
7+7 = 14
= 4:14
Pressley is working two part-time jobs. He makes $18 per hour lifeguarding and $12 per
hour as a cashier at the local grocery store. During spring break from school, he worked
twice as many hours lifeguarding as he did at the local grocery store and earned $144.
How many hours did he work at each job?
Answer: He spent 3 hours as a cashier and 6 hours as a lifeguard
Step-by-step explanation:
First, you figure out his time as a cashier; 12($ per hour) x 3(hours working) = $36. Then, since it states he spent twice as many hours being a lifeguard, you double his hours when figuring out his time as a lifeguard; 18($ per hour) x 6(hours working) = $108. Add up both of your totals, $108 + $36 = $144.
i need help plssssssssssss
Answer:
I can't well see question but, their ratios aren't the same
HELP ASAP PLEASE WITH EXPLINATION!!
Chris earns $7.00 per hour working on the weekends he needs at least $210.00 for a new cell phone. How many hours, h, doe Chris need to work on the weekends to buy a new phone
Answer:
So...
Step-by-step explanation:
He earns $7.00 per hour, and he needs $210.00. H represents hours.
7.00 every hour
So 7.00 x 2 is 14
7.00 x 10.00 is 70
7.00 x 30 is 210. So after 30 hours he will be able to buy his phone. He should buy his phone on black friday. But now its too late.
Write the equation of the line passing through the points (-1,9) and (-9,1).
The equation of the line is…
Answer:
y=x+10Step-by-step explanation:
m=y2- y1/x2 -x1y2=1,y1=9,x2=-9,x1= -1m=1 -9/-9-(-1)m=1m= y-y1/x-x11 =y- 9/x -(-1)y-9 =x+1y =X +102x2−4x=t In the equation above, t is a constant. If the equation has no real solutions, which of the following could be the value of t ?A. −3
B. −1
C. 1
D. 3
The correct option A. -3, is the value of constant 't', for which the equation has no real solutions.
Define the term real solutions?In algebra, a real solution is just an answer to an equation which is a real number. The number of solutions to the provided quadratic equation depends on the discriminant, but can be positive, 0, or negative. A quadratic equation with a positive discriminant has two unique real number solutions.A repeating real number solution to the quadratic equation is indicated by a discriminant of zero.For the stated question-
The quadratic equation is given as-
2x² - 4x = t
2x² - 4x - t = 0
The standard from of quadratic equation is-
ax² + bx + c = 0
For no solution;
Discriminant is less than zero.
D < 0
b² - 4ac < 0
Comparing both equations-
b = -4, a = 2 and c = -t
Put value in D.
(-4)² - 4(2)t < 0
Solve the inequality
16 - 8t < 0
t < -2
Thus, the value of constant 't', for which the equation has no real solutions.
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The correct question is-
2x² - 4x = t,In the equation above, t is a constant. If the equation has no real solutions, which of the following could be the value of t ?
A. -3
B. -1
C. 1
what is the answer to -2a+5a=-3a
Answer: a=0
Step-by-step explanation:
-2a + 5a = -3a
3a = -3a
a= 0
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what is the value of x in this triangle? enter your answer in the box. x
By using trigonometry, it can be calculated that
Value of x is 23.775
What is trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions. They are
[tex]sin \theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]
[tex]sin\theta = \frac{perpendicular}{hypotenuse}[/tex]
[tex]cos\theta = \frac{base}{hypotenuse}[/tex]
[tex]tan\theta = \frac{perpendicular}{base}[/tex]
[tex]cot\theta = \frac{base}{perpendicular}[/tex]
[tex]sec\theta = \frac{hypotenuse}{base}[/tex]
[tex]cosec\theta = \frac{hypotenuse}{perpendicular}[/tex]
Trigonometry is a very important tool in mathematics.
Here, trigonometry is used
From the figure,
cos 18 = [tex]\frac{x}{25}[/tex]
0.951 = [tex]\frac{x}{25}[/tex]
x = 0.951 [tex]\times[/tex]25
x = 23.775 cm
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Complete Question
what is the value of x in this triangle? enter your answer in the box. x
x = cm
A right triangle. The hypotenuse is labeled as 25 centimeters. The base is labeled as x. The alternate base angles are labeled as right angle and 18 degrees, respectively.
Write an equation in point-slope form for the line that passes through the point with the given slope. (–2, 11).m=4/3
Answer:
y
+
2
=
3
4
(
x
−
11
)
Explanation:
Point slope form is given by the following formula:
y
−
y
1
=
m
(
x
−
x
1
)
In order to use the point slope formula we need two things:
1. The slope or
m
which in this case is
4
3
2. A point on the graph which we are given
(
−
2
,
11
)
Along with the slope, if we let
(
−
2
,
11
)
→
(
x
1
,
y
1
)
we can substitute all this information into the point-slope formula:
y
−
−
2
=
3
4
(
x
−
11
)
Simplify:
y
+
2
=
3
4
(
x
−
11
)
hope I helped you:)
Solve a.
a+4/5= 1 1/2
Answer:
Step-by-step explanation:
a+4/5=11/2
-4/5. -4/5
_____. _____
a= 11/2 *5/5. = 55/10
-4/5 * 2/2. -8/10
______________
a= 47/10
Solve for y given that the height of the triangle is 4 miles and each of the legs are 7 miles.
Answer:
Step-by-step explanation:
x^2 + y^2 = z^2 is the pythagorean theorem.
If you divide the large triangle into two separate ones, with sides 7, 4 and 0.5y, you can use the pythagorean theorem to figure out 0.5y. So:
7^2 = 4^2 +(0.5y)^2
49-16 = 33
so y=2sqrt(33)
what is the area of semicircle if the arc is 35 pi
Answer:
612½ pi units² or 1920 units²
maya drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took hours. when maya drove home, there was no traffic and the trip only took hours. if her average rate was miles per hour faster on the trip home, how far away does maya live from the mountains? do not do any rounding.
Maya drove on the mountains for her trip. Due to traffic, her average rate of miles per hour was faster at the time of coming back to her home than going on her trip. Thus, The distance between where she lives and the mountains is
288 miles .
Let's consider that Maya live x miles from the mountains.
Let her rate to mountains be y miles/h.
we have given that
Driveing time taken by Maya going from home to trip location= 9 hours due to traffic
total return time taken by her = 4 hours
average rate = 40 miles/hour
Using rate formula,
Rate = distance/time
=> distance (d) = rate (r) × time (t)
so, x/y = 9
=> x=9y --(1)
Return trip 4 hours then rate = y+40
=> x/(y+40) =4 --(2)
using Substitution method, x= 3 substitute in (2)
=> 9y/(y+40)=4
=> 9y=4y+160
=> 9y-4y=160
=> 5y=160
=> y= 160/5
=> y=32
Now, x=9y
x=9×32= 288 miles
Hence, distance to the mountain is 288 miles.
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Complete question:
Maria drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 9 hours. When Maria drove home, there was no traffic and the trip only took 4 hours. If her average rate was 40 miles per hour faster on the trip home, how far away does Maria live from the mountains?
Do not do any rounding.
Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots and 2?.
On solving the given question, we got that - the polynomial function of lowest degree with rational real coefficients is [tex]= > P(x) = 3x^{2} - 21x + 30[/tex]
What is Polynomial Equation?Polynomial equations are those created using variables, exponents, and coefficients. The higher exponent, known as the equation's degree, can have a variety of exponents. By factoring polynomials based on the degree and variables in the equation, we can solve them.
We are aware that the lowest degree polynomial function, denoted by p(x), has the following properties:
[tex]= > P(x) = c(x - a)(x - b)\\[/tex]
The leading coefficient is 3, the roots are 5, and the roots are 2, respectively.
Therefore, the lowest degree polynomial with the aforementioned characteristics is:
[tex]= > P(x) = 3(x - 5)(x - 2))\\= > P(x) = 3(x^{2} - 7x + 10)\\= > P(x) = 3x^{2} - 21x + 30\\[/tex]
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UGGGHHHH! THIS IS FIND SLOPE INTERCEPT AND I CAN’T FIGURE IT OUT!
The linear equation written in the slope-intercept form is:
y = -x - 5
How to find the slope?A linear equation can be written in the slope-intercept form as:
y = m*x + b
Where m is the slope and b is the y-intercept.
Particularly, if the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope of the line is written as:
m = (y₂ - y₁)/(x₂ - x₁)
Here we can use the first two points on the table (or any you want) to find the slope:
(-1, -4) and (3, -8)
m = (-8 + 4)/(3 + 1) = -1
The slope is -1, so the line is something like:
y = -x + b
To find the value of b we can use another of the points on the table, if we use (7, -12) then we must have:
-12 = -7 + b
-12 + 7 = b
-5 = b
The linear equation is:
y = -x - 5
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simplify (−4r5)(2r8)
Answer: -8r^13
Step-by-step explanation: We just need to take those numbers multiplied by each other. -4 timed 2 = -8. r^5 timed r^8 = r^13, we just add both because they have the same base and multiple a square is the same as adding them together.
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3) The 10th term in the expansion of (4x - 2y)11
Answer:
57671680x^9 y^2
Step-by-step explanation:
using combinatorics
Help me......Solve for each variable. Show your work and explain in paragraph form how you solved each problem.
Base Angles Theorem
Converse to Base Angles Theorem
Corollary
Converse to the corollary
Sum of Interior Angles
Exterior angles
1) The value of x is 30 degree.
2) The value of x is 32.5 degree.
What is Base Angle Theorem?A triangle's opposite angles are also congruent if its two sides are.
Given:
Using Base Angle Theorem
Two Angles are 35 and 35.
Using Angle Sum Property
3x+ 20 +35+ 35 = 180
3x+ 90 = 180
3x = 90
x= 30
Again Using Base Angle Theorem
let the Angles in left triangle are 50, y and y
Using Angle Sum Property
50+ 2y= 180
2y= 130
y= 65
Again Using Angle Sum Property in Big Triangle
50+x + 65 + x = 180
2x = 65
x= 32.5 degree
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Use the fact that the trigonometric functions are periodic to find the exact value of the given expression. Do not use a calculator.
sec.(25π/4)
Subtract full rotations of 2π until the angle is greater than or equal to 0 and less than 2π
sec(π4) – trigonometry value
The exact value of trigonometry - sec(π4) is 2√2.
Multiply 2√2 by √2.
2⋅√2⋅2
Combine and simplify the denominator.
2√2
Cancel the common factor of 2.
√2
There are various ways to display the outcome.
Exact Form:
√2
Decimal Form:
1.41421356…
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mapped a quadrilateral on a coordinate plane. If she plots one segment from (–3, –3) to (3, 9) and another segment from (–5, 12) to (1, 0), are the segments parallel? Justify your reasoning.
The line segments joining the given points are not parallel.
How to find the slope of a line?In order to find the slope of a line, calculate the angle it makes with x axis as a reference. Then its slope can be determined by taking tan ratio of that angle.
Given that,
The first segment is joined from (3, -3) to (3, 9).
And, the second segment is joined from (-5, 12) to (1, 0).
In order for the segments to be parallel, their slope must be equal.
The slopes of both the segments can be found as,
First segment,
Slope = (3 - 3)/(-3 - 9)
= 0/-12
= 0
Second segment,
Slope = (-5 - 1)/(12 - 0)
= -6/12
= -1/2
Since slopes of the segments are not equal, they are not parallel.
Hence, the given line segments are not parallel.
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In tryouts for the olympics, a speed skater had times of 44. 64, 43. 45, 42. 79, and 42. 28 seconds. Find the average time. (hint: add the numbers and divide by 4. ).
The average time of the Olympic speedskated is 43.29 units.
What do we mean by average?An average, which is frequently the sum of the numbers divided by the total number of the numbers in the group, is a single number that is selected to describe a group of numbers in simple English.
For example, the average of the numbers 2, 3, 4, 7, and 9 is 5.
The four sorts of averages that we recognize are mean, mode, median, and range.
Although the others are our most popular "measures of central tendency," range is actually a measure of spread or distribution.
So, the average time is calculated as follows:
We have: Time: 44.64,43.45,42.79 and 42.28
The formula for average mean: ∑ₓ/n
Where ∑ₓ is the sum of observations and n is the number of observations.
Now, calculate the average time:
Average = 44.64+43.45+42.79+42.28/4
Average = 173.16/4
Average = 43.29
Therefore, the average time of the Olympic speedskated is 43.29 units.
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Colton sold a total of 28 t-shirts and sweatshirts as part of a fundraiser for his football team. If t-shirts cost $12 each and sweatshirts cost $20 each and he raised a total of $424, how many †-shirts did he sell?
i need points
Step-by-step explanation:
One week, magan earned $162. 00 at his job when he worked for 9 hours. If he is paid the same hourly wage, how much would he make the next week if he worked 19 hours?.
Answer: $342
Step-by-step explanation:
We take 162.00 divided by 9 = $18 / h
To find the salary of 19 hours we just need to take 18 times 19 = $342
Nia's normal running
route is 3 1/3 miles.
If she ran this route 3 3/4 times
this week, find the total
number of miles she ran.
What is the solution of the system of equations? Explain.
y = x +4
2
2y + 4 = x
The solution of the system of equations:
y = x + 422
y + 4 =x
is the point (-88, -46)
How to solve the system of equations?Here we have the system of equations:
y = x + 42
2y + 4 =x
To solve the system, we can replace the first equation into the second one:
2*(x + 42) + 4 = x
2x + 84 + 4 = x
2x + 88 = x
2x - x = -88
x = -88
And the value of y is:
y = x + 42
y = -88 + 42 = -46
The solution is the point (-88, -46).
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A casino only has red playing chips for $10 each and blue playing chips for $5 each. Jack paid $400 to purchase 50 playing chips at the cashier's window. How many red playing chips were given to him?
Answer: 30
Step-by-step explanation:
1 red chip = $10, so 30 red chips = $ 300
1 blue chip = $5, so 20 blue chips = $100
Add the cost of both we get $400, matching our question requirements.
Percentage,base,rate
Answer:125
Step-by-step explanation: