We were given the following details:
This is a normal distribution. Normal distributions are solved using the z-score
[tex]\begin{gathered} \mu=5min \\ \sigma=3min \end{gathered}[/tex]The z-score for a value, X is calculated using the formula:
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ The\text{ probability that a person will wait more than 1 minute implies that: }X=1 \\ Z=\frac{1-5}{3} \\ Z=-\frac{4}{3} \\ At\text{ Z =}-\frac{4}{3}\text{, pvalue =}0.091759 \\ The\text{ probability that a person waits more than 1 minute is given by:} \\ P=1-0.091759 \\ P=0.908241\approx0.9082 \\ P=0.9082\text{ or }90.82\text{\%} \end{gathered}[/tex]As a town gets smaller, the population of its high school decreases 6% each year. The senior class has 320 students now. In how many years will the high school have 100 students?
From the details provided, we know that the population of the town gets smaller, that is, a decline and not a growth. The annual rate of decline (or decay) is 6% (or 0.06). The formula for this is given as shown below;
[tex]y=a(1-r)^x_{}[/tex]The variables here are;
[tex]\begin{gathered} a=\text{initial value} \\ r=\text{rate of decline} \\ x=\text{period (in years)} \end{gathered}[/tex]The equation to represent the decline of this town's student population shall be;
[tex]\begin{gathered} y=320(1-0.06)^n \\ Simplified,\text{ we now have;} \\ y=320(0.94)^n \end{gathered}[/tex]When the population ofnthe town becomes 100, then we can replace variable y with 100. Since the formula is used to find the current population, and we have been given the population after a certain number of years, then our y is now 100.
We can now determine the number of years (variable n) that it takes before the population declines to 100 as shown below;
then our y is now 100.
We can now
Tyler said he swam 23 tenths miles this week. His coach said Tyler swam 2.3 miles this week. To find who is correct, model the distance both Tyler and his coach said Tyler swam. Use the flat as 1 unit. A: What do you need to use?B: What do you know about representing whole numbers and decimals that may help you solve the problem? C: Complete the sentencesAre the models alike or different?Tyler swam _____ tenths, or _____, miles.So, _____________________ are correct.
Answer with explanation:
We need to determine if what Tyler is saying is in fact equal to what his coach said, to get the final answer, we have to concert the resulting units in miles:
Taylor's answer:
[tex]23\times(\frac{1}{10})\text{ miles}\Rightarrow(\frac{23}{10})\text{miles}\Rightarrow2.3\text{ miles}[/tex]Coach's answer:
[tex]2.3\text{ miles}[/tex]In conclusion, The two answers are correct so the two models are indeed alike.
Valentina earned some money doing odd jobs last summer and put it in a savings account that earns 7% interest compounded quarterly after 5 years there is 500.00 in the account how much did valentina earn doing odd jobs
use prowers and multiplication to write the equation whose value is 10 to the 11th power
if we have
(10^9)(10^2)
adds the exponents
10^(9+2)
10^11
If you have
10^18/ 10^7
subtract the exponents
10^(18-7)
10^11
If you have
(10^6)^2/10
First multiply the exponents
10^(6*2)/10
10^12/10
subtract exponents
10^(12-1)
10^11
A study found that 36% of the assisted reproductive technology (ART) cycles resulted in pregnancies. Twenty-six percent of the ART pregnancies resulted in multiple births. (a) Find the probability that a random selected ART cycle resulted in a pregnancy and produced a multiple birth. (b) Find the probability that a randomly selected ART cycle that resulted in a pregnancy did not produce a multiple birth.(c) Would it be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
assisted reproductive technology (ART) cycles:
pregnancies = 36%
pregnancies resulted in multiple births = 26%
Step 02:
a.
p (pregnancies) = 36% = 36/100 = 0.36
pregnancies resulted in multiple births = 26% = 26/100 = 0.26
p(pregnancies resulted in multiple births) = 0.36*0.26 = 0.0936
b.
p (pregnancy did not produce a multiple birth) = 1 - 0.0936 = 0.9064
c.
Indeed, the probability of multiple pregnancies is low 9.36%.
That is the full solution.
Question
Find the values for x and y .
Step-by-step explanation:
6x+3=75° ( being alternate angle )
6x = 72°
x=12
75+45+y= 180
y= 60°
Two lines intersect in the diagram shown below. 127° to What is the value of x? Hide All 37 53 127 D 217 O
x=127º
1) Since those angles x, and 127º share a common vertex we can state that these are Vertical Angles
2) Therefore they are congruent to each other. And we can state:
x = 127º as well.
A decorator creates a scale drawing of a dinning room table. The length of the scale is 3 centimeters. The image represents the dimensions of the actual dinning room table. What is the area of the scale drawing?
From the image given, the dinning room table is a rectangle.
Given:
Length in inches = 90 inches
Width in inches = 45 inches
The scale of the length is 3 centimeters.
Now, let's find the scale of the table:
[tex]\frac{90}{3}=30\text{inches}[/tex]This means that 30 inches represents 1 centimeter.
Also, let's find the width in centimeters:
[tex]\frac{45}{30}=1.5\operatorname{cm}[/tex]Thus, we have:
Length of scale drawing = 3 cm
Width of scale = 1.5 cm
To find the Area of the scale drawing, use the area of a rectangle:
A = Length x Width
[tex]A=3\times1.5=4.5\operatorname{cm}^2[/tex]Therefore, the length of the scale drwing is = 4.5 cm²
ANSWER:
[tex]4.5\operatorname{cm}^2[/tex]Hey can you please help me with this question and please may sure the answer correctly
Option C is the answer
A class had a quiz where scores ranged from 0 to 10.N(s) models the number of students whose score on the quiz was s.What does the statement N(8) > N(5) mean?Group of answer choicesA score of 8 is greater than a score of 5.There are more students who scored 8 than students who scored 5.There are 8 students who scored higher than 5.
The expression N(s) models the number of students that got a score "s" on the quiz.
Then the expression N(8) represents the number of students that scored 8 on the quiz.
And N(5) represents the number of students that scored 5 on the quiz.
[tex]N(8)>N(5)[/tex]Can be read as: "The number of students whose score on the quiz was 8 is greater than the number of students whose score on the quiz was 5"
Therefore, you can conclude that there were more students who scored 8 than students who scored 5. (option 2)
is 6x0=O and example of distributive property?
we have that
Distributive property is the product of a factor and a sum (or difference) equals the sum (or difference) of the product
In this exanple
6x*0=0
Is not the product of a factor and a sum or difference
Patient Smith was on a diet. He weighed 122.6 kilograms. After one month he weighed 112.8 kilograms. Whatwas his total weight loss in one month?
If Smith uses both medications, then its dosage is the sum of each.
[tex]\text{total dosage = 48.5 + 0.5 = 4}9\text{ ml}[/tex]The total dosage of the medication would be 49 ml if he got both medications.
What is the length of the dotted line in the diagram below? Round to the
nearest tenth.
Answer:
12.1 units
Step-by-step explanation:
the remainder when f(x)is divided by x-3 is 15. Does f(-3) =15? explain why or why not
We will see that the function f(x) is:
f(x) = 15*(x - 3)
Evaluating it in x = -3 we can see that:
f(-3) = -90
Is the statement true?We know that when we divide f(x) by (x - 3), the quotient is 15. (that is the statement given in the question)
so we can write the equation:
f(x)/(x - 3) = 15
And we can solve this for f(x) as if it were a variable, then we get:
f(x) = 15*(x - 3)
Now, if we evaluate the function in x = -3 (this is replacing the variable x with the number -3), we will get:
f(-3) = 15*(-3 - 3) = 15*(-6) = -90
So the statement:
f(-3) = 15
Is false
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Issac says that T' will be located at (4,20)Isabella says that T' will be located at (4,12(who is correct and why?
In the given triangle :
The coordinate of T is ( 2, 10 )
Triangle TUV will be dilated by a scale factor of 2
Thus, multiply the coordinates of TUV by 2
T' = 2 x T
T' = 2 x ( 2, 10 )
T' = ( 2x2, 2x10)
T' = ( 4, 20 )
So, T' will be located at ( 4, 20 )
Issac says that T' will be located at (4,20)
Answer : Issac says that T' will be located at (4,20)
The function g is defined as follows for the domain given g(x) = 3x - 2 , omain = \{- 2, - 1, 0, 1\} Write the range of g using set notation. Then graph g
Given: The function below
[tex]\begin{gathered} g(x)=3x-2 \\ Domain:\lbrace-2,-1,-0,1\rbrace \end{gathered}[/tex]To Determine: The range and the graph of g
Solution
The range is as given below
[tex]\begin{gathered} x=-2 \\ g(-2)=3(-2)-2=-6-2=-8 \\ x=-1 \\ g(-1)=3(-1)-2=-3-2=-5 \end{gathered}[/tex][tex]\begin{gathered} x=0 \\ g(0)=3(0)-2=0-2=-2 \\ x=1 \\ g(1)=3(1)-2=3-2=1 \end{gathered}[/tex]Hence, the range is
{-8, -5, -2, 1}
Let us form a table showing the domain(x) and the range (g(x))
Let us use the table to plot graph of the domain(x) against the range(g(x)) as below
two factor of 2=2²two factor of 3=3²
Exponents indicate how many times a number is multiplied by itself
Two factor two= 2*2= 2²=4
Two factor of three is 3*3=3²=9
A plane intersects both bases of a cylinder, passing through the center of each baseof the cylinder. What geometric figure will be formed from this intersection?
When a plane intersects both bases of a cylinder, passing through the center of each base of the cylinder, the cross section formed is a rectangle.
Line segment MN is the image of CD after a dilation by a factor k with a center at point A. Using your ruler, determine the value of k to the nearest hundredth. Show the work that leads to your answer.
Methjod th find the asnswer to thsi question.
First of mark a point on the line segment CD. Then, draw a perpendicular from that point to the a point to the line segment MN.
Then, mesure the length of the line segment.
Thus, the value of k is obtained.
A rectangular pool is 7 meters wide and 12 meters long. If you swim diagonally from one corner to the other, how many meters will you swim? Approximate the answer to the nearest tenth.
Answer: 15cm
Step-by-step explanation:
Your welcome
A beach ball rolls off a cliff and onto the beach. The height, in feet, of the beach ball can be modeled by the function h(t)=64−16t2, where t represents time, in seconds.What is the average rate of change in the height, in feet per second, during the first 1.25 seconds that the beach ball is in the air?Enter your answer as a number, like this: 42
STEP - BY - STEP EXPLANATION
What to find?
The average rate of change in the height, in feet per second, during the first 1.25 seconds that the beach ball is in the air.
Given:
[tex]h(t)=64-16t^2[/tex]Step 1
Differentiate the heigh with reospect to t.
The rate of change of height is the differentiation of the height.
[tex]\frac{dh(t)}{dt}=-32t[/tex]Step 2
Substitute t= 1.25
[tex]h^{\prime}(t)=-32(1.25)[/tex][tex]=-40ft\text{ /s}[/tex]ANSWER
Average rate = -40 ft / s
Given:• UZ | VW• UV ZUZ306Nw4511Which is closest to mZW?26.630°60°63.49
From the image, given that UZ is parallel to VW, UV is congruent to UZ. We can redraw the image to include some extra details.
The image is below;
With the image above, we can the find the angle W, using tangent function of trigonometry.
This is seen below;
[tex]\begin{gathered} \tan w=\frac{opposite}{\text{Adjacent}} \\ \text{opposite =30ft} \\ \text{Adjacent}=15ft \\ \therefore\tan w=\frac{30}{15} \\ \tan w=2 \\ w=\tan ^{-1}2 \\ w=63.4^0 \end{gathered}[/tex]The angle closest to m
Answer: 63.4
why does a cubic graph have both an x intercept and a y intercept
Answer:
All cubic function has domain (-∞,∞) and range (-∞,∞)
Step-by-step explanation:
If f(x) = -3 and g(x) = 4x + 2x - 4, find (* + )(x).O A. 4x2 + x +1OB. 432 + x ->C.X2-12OD. 4x2+2x-7
You have the following functions:
[tex]\begin{gathered} f(x)=\frac{x}{4}-3 \\ g(x)=4x^2+2x-4 \end{gathered}[/tex]In order to find (g + f)(x) add like terms of each function. Remind that like terms are those terms with the same variable and same exponent.
Then, you have:
[tex]\begin{gathered} (f+g)(x)=4x^2+2x+\frac{x}{4}-3-4 \\ (f+g)(x)=4x^2+\frac{9}{4}x-7 \end{gathered}[/tex]Hence, the answer is
4x^2 + 9/4 x - 7
Use the distance formula to find the distance between the points given.(-9,3), (7, -6)
Given the points:
[tex](-9,3),(7,-6)[/tex]You need to use the formula for calculating the distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1^})^2[/tex]Where the points are:
[tex]\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}[/tex]In this case, you can set up that:
[tex]\begin{gathered} x_2=7 \\ x_1=-9 \\ y_2=-6 \\ y_1=3 \end{gathered}[/tex]Then, you can substitute values into the formula and evaluate:
[tex]d=\sqrt{(7-(-9))^2+(-6-3)^2}[/tex][tex]d=\sqrt{(7+9)^2+(-9)^2}[/tex][tex]d=\sqrt{(16)^2+(-9)^2}[/tex][tex]d=\sqrt{256+81}[/tex][tex]d=\sqrt{337}[/tex][tex]d\approx18.36[/tex]Hence, the answer is:
[tex]d\approx18.36[/tex]Help me pleaseeee quicklyyyyy
∠6 and ∠5 are alternative interior angle thus the measure of angles ∠5 = 45° , ∠6 = 45° ,∠7 = 45° and ∠8 = 135°.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
Angles 1,2,7 are the interior angles of a triangle and we know that the sum of all interior angles inside a triangle is 180°.
Therefore, ∠1 + ∠2 + ∠7 = 180°
Given, ∠1 = 70° and ∠2 = 65°
∠7 = 180° - (70 + 65) = 45°
Now, ∠8 = 180 - ∠7 ⇒ ∠8 = 135°
Now, ∠7 = ∠6 (vertical opposite angle) so ∠6 = 45°
∠6 = ∠5 (alternative interior angle) so ∠5 = 45°
Hence "∠6 and ∠5 are alternative interior angle thus the measure of angles ∠5 = 45° , ∠6 = 45° ,∠7 = 45° and ∠8 = 135°".
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Bentley has 32 biscuits left in his treat jar. If this represents 4/5 of what he orginally had in the jar, how may treats did he have in the beginning
he had 40 biscuits in the beginning
Explanation
to solve this we can use a rule of three
so
Step 1
let x represents the total treats he had in the beginning , so
[tex]\begin{gathered} if \\ 32\text{ biscuits}\rightarrow\frac{4}{5}of\text{ total } \\ then \\ x\text{ biscuits}\rightarrow total\text{ \lparen1\rparen} \end{gathered}[/tex]so, the proportion is
[tex]\begin{gathered} \frac{32}{\frac{4}{5}\text{ }}=\frac{x}{1} \\ \frac{160}{4}=x \\ x=40 \end{gathered}[/tex]therefore,
he had 40 biscuits in the beginning
I hope this helps you
If we use 3.14 for pi, describe the ratio between the circumference and the diameter of a circle.
Solution
The ratio of the circumference of any circle to the diameter of that circle.
[tex]\begin{gathered} \text{circumference of a circle=}\pi d \\ \text{where d is the diameter} \\ \\ \text{circumference of a circle=3.14}d \end{gathered}[/tex]The ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi.
2x^3-16x^2-40x=0 factor
The given expression is
[tex]2x^3-16x^2-40x=0[/tex]We extract the common factor 2x.
[tex]\begin{gathered} 2x(x^2-8x-20)=0 \\ 2x=0\rightarrow x=0 \\ x^2-8x-20=0 \end{gathered}[/tex]The first solution is 0.
Now, we solve the quadratic expression. We have to find two numbers whose product 20 and whose difference is 8. Those numbers are 10 and 2.
[tex]x^2-8x-20=(x-10)(x+2)[/tex]Hence, the given expressions expressed, as factors, is[tex]2x^3-16x^2-40x=x(x-10)(x+2)[/tex]Given the following function, find f(-3), f(0), and f (2) f(x)=5x-2
The output values of f(-3), f(0) and f(2) of the function f( x ) = 5x - 2 are -17, -2 and 8 respectively.
What are the output values of f(-3), f(0) and f(2) in the given function?A function is simply a relationship that maps one input to one output.
Given the data in the question;
f( x ) = 5x - 2f( -3 ) = ?f( 0 ) = ?f( 2 ) = ?For f( - 3 );
To find the output value of f( -3 ), replace all the occurrence of x with -3 in the function and simplify.
f( x ) = 5x - 2
f( -3 ) = 5(-3) - 2
f( -3 ) = -15 - 2
f( -3 ) = -17
For f( 0 );
To find the output value of f( 0 ), replace all the occurrence of x with 0 in the function and simplify.
f( x ) = 5x - 2
f( 0 ) = 5(0) - 2
f( 0 ) = 0 - 2
f( 0 ) = -2
For f( 2 );
To find the output value of f( 2 ), replace all the occurrence of x with 2 in the function and simplify.
f( x ) = 5x - 2
f( 2 ) = 5(2) - 2
f( 2 ) = 10 - 2
f( 2 ) = 8
Therefore, the output value of f( 2 ) is 8, this forms an ordered pair of ( 2, 8 ).
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