The fraction equivalent to 3/8 with a numerator and denominator product of 216 is 9/24.
To find the fraction equivalent to 3/8 with a numerator and denominator product of 216, follow these steps:
Set up an equation for the product of the numerator and denominator:
x × y = 216.
Since the fraction is equivalent to 3/8, you can write another equation: x / y = 3/8.
Solve for x in terms of y in the second equation:
x = (3/8) × y.
Substitute this expression for x in the first equation:
(3/8) × y × y = 216.
Solve for y: [tex]y^2 = (8/3) × 216.[/tex]
Simplify the equation: y^2 = 576.
Find the square root of both sides: y = 24.
Now, find x using the equation x = (3/8) × y:
x = (3/8) × 24.
Simplify the expression:
x = 9.
So, the fraction equivalent to 3/8 with a numerator and denominator product of 216 is 9/24.
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stratified random sampling is a method of selecting a sample in which . a. the population is first divided into groups, and then random samples are drawn from each group b. the elements are selected on the basis of convenience c. various strata are selected from the sample
The stratified random sampling is a method of various strata are selected from the sample. So, the right choice for answer is option(c).
The four probability sampling methods mainly applied in research methods include simple random sampling, cluster sampling, stratified sampling, and systematic sampling. In certain situations, we need to remove the sampling bias, and for that, we opt for stratified random sampling. Here we talking about stratified random sampling. A method of probability sampling (where all members of the population have an equal chance of being included) Population is divided into 'strata' (sub populations) and random samples are drawn from each. Therefore, the required choice is option (c), that is various strata are selected from the sample.
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Brooklyn is going to an amusement park. The price of admission into the park is $10, and once she is inside the park, she will have to pay $3 for every ride she rides on. How much money would Brooklyn have to pay in total if she goes on 11 rides? How much would she have to pay if she goes on � r rides?
Brooklyn have to pay total for the 11 rides is $43 and for r rides she have to pay is $10+$3×r.
If Brooklyn goes on 11 rides, she will have to pay $10 for admission and $3 for each of the 11 rides she goes on. So her total cost would be:
$10 + (11 rides x $3/ride) = $10 + $33 = $43
If she goes on r rides, her total cost would be:
$10 + (r rides x $3/ride) = $10 + $3r
So, for example, if she goes on 15 rides, her total cost would be:
$10 + (15 rides x $3/ride) = $10 + $45 = $55
An arithmetic expression is a combination of numbers, operators (such as +, -, x, ÷), and parentheses that can be evaluated to produce a numerical result.
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lester jarred 30 liters of jam after 3 days. how many does lester need to spend making jam if he wants jar 40 liters of jam in all? solve using unit rates
Thus, it will take 4 days time for the Lester to spend on preparing the jar of 40 liters of jam.
Explain about the proportion of numbers:If we were to assume that we had any two quantities (as well as 2 entities) and that we were tasked with figuring out their ratio, the ratio formula would be defined as a: where b = a/b
Any two numbers could constitute a and b.The initial term or antecedent is "a."The second phrase or consequent is "b."Given data:
Time to jam 30 liters ---> 3 days.
Time to jam 40 litres ---> x days (say)
Then, taking the proportion,
30 lit / 3 day = 40 lit / x days
x = 3*40 / 30 days
x = 4 days
Thus, it will take 4 days for the Lester to spend on preparing the jar of 40 liters of jam.
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Find the measure of the missing angle and arc
It is important to carefully read and understand the information given in the problem, as well as to apply the appropriate formulas and properties to find the solution
Sure, I'll be happy to help you with your question. In order to find the measure of the missing angle and arc, we first need to know what type of angle and arc we are dealing with. If it is a central angle and arc, then the measure of the angle is equal to the measure of the arc. However, if it is an inscribed angle and arc, then the measure of the angle is half the measure of the arc.
Once we have determined the type of angle and arc, we can use the given information to solve for the missing measure. For example, if we are given the measure of the angle and the measure of the arc, we can use the formula for the measure of a central angle or inscribed angle to solve for the missing measure.
Alternatively, we can also use the properties of circles, such as the fact that the sum of the angles in a triangle is 180 degrees and the fact that the angle at the center of a circle is twice the angle at the circumference, to solve for the missing measure.
In any case, . With enough practice and familiarity with these concepts, you can become proficient at solving problems involving missing angles and arcs.
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A different coffee shop called Ruth's Roast's serves drinks that contain a mean of 16g of sugar with a standard deviation of 6g. A Grande Mocha Cappuccino at Ruth's Roast's contains 13g of sugar.
Assuming that the distribution center of sugar amounts have approximately the same shape, at which shop does this drink have less sugar relative to the other drinks at its respective store?
Based on the calculations using z-scores, we can conclude that the Grande Mocha Cappuccino at Ruth's Roast's has less sugar relative to the other drinks at its respective store than the Grande Mocha Cappuccino at Coffee Haven.
What is Coffee Haven?
"Coffee Haven" was used as an example name for one of the coffee shops in a previous question. It is not an actual coffee shop. The name was used to illustrate a point about comparing the sugar content of drinks between different coffee shops.
To compare the sugar content of the Grande Mocha Cappuccino between the two coffee shops, we can use z-scores to standardize the sugar content based on the mean and standard deviation of each shop's drinks.
For the first coffee shop, let's call it Coffee Haven, we know that the mean sugar content is 20g with a standard deviation of 8g. Therefore, the z-score for the Grande Mocha Cappuccino at Coffee Haven is:
z = (13 - 20) / 8 = -0.875
For the second coffee shop, Ruth's Roast's, we know that the mean sugar content is 16g with a standard deviation of 6g. Therefore, the z-score for the Grande Mocha Cappuccino at Ruth's Roast's is:
z = (13 - 16) / 6 = -0.5
Comparing the two z-scores, we see that the z-score for the Grande Mocha Cappuccino at Ruth's Roast's is greater than the z-score for the Grande Mocha Cappuccino at Coffee Haven. This means that the Grande Mocha Cappuccino at Ruth's Roast's has less sugar relative to the other drinks at its respective store than the Grande Mocha Cappuccino at Coffee Haven.
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Assume that women's weights are normally distributed with a mean given by μ=143 lb and a standard deviation given by σ=29lb.
(a) If 1 woman is randomly selected, find the probabity that her weight is above
176
(b) If 4 women are randomly selected, find the probability that they have a mean weight above 176
(c) If 57women are randomly selected, find the probability that they have a mean weight above 176
Answer:
a) 0.128 b) 0.51 c) 7.27
Step-by-step explanation:
a)
Lower Bound: 176
Upper Bound: 99999
μ: 143
σ: 29
= 0.1275….
b)
Lower Bound: 176
Upper Bound: 99999
μ: 143
σ: 29
0.1275… (4) = 0.51
c)
Lower Bound: 176
Upper Bound: 99999
μ: 143
σ: 29
0.1275… (57) = 7.27
Find the distance between $\left(15,-17\right)$ and $\left(-20,-5\right)$ .
The distance between the points (15, -17) and (-20, -5) is 37.
What is distance formula?The distance formula is a mathematical formula used to find the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and can be used to find the distance between any two points, whether they are on the same line or on different lines.
We can use the distance formula to find the distance between two points:
[tex]\rm d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
Let [tex]\rm (x_1,y_1)[/tex] = (15,-17) and [tex]\rm (x_2, y_2)[/tex] = (-20,-5)
Then, plugging into the formula, we get:
[tex]\rm d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
[tex]\rm = \sqrt{(-20-15)^2 + (-5-(-17))^2}[/tex]
[tex]= \sqrt{(-35)^2 + (12)^2}[/tex]
[tex]= \sqrt{1225+144}[/tex]
[tex]= \sqrt{1369}[/tex]
= 37
Therefore, the distance between the points (15, -17) and (-20, -5) is 37.
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Complete question:
Find the distance between point (15,-17) and (-20,-5).
Question 2-5 Use the following information to answer Part A and Part B. A population of birds can be represented by a quadratic function where t represents the time in months since the birds were first co birds. This function can be represented with three equivalent forms. Part A Inline Drop Down: 1 point for answer only mit Test B=-0.4(t+10)(1-350) B=-0.412+1361+1400 Which form reveals the number of birds present on the island when counting first started? B=-0.412+1361+140 B =
According to given c represents the initial number οf birds οn the island
What is a quadratic equatiοn?A pοlynοmial οf degree twο in οne οr mοre variables is referred tο as a quadratic pοlynοmial. The pοlynοmial functiοn that a quadratic pοlynοmial defines is knοwn as a quadratic functiοn.
functiοn represents a quadratic mοdel fοr the bird pοpulatiοn, we can write it in standard fοrm as:
f(t) = at² + bt + c
where a, b, and c are cοnstants.
Substituting t = 0 in the standard fοrm οf the quadratic functiοn, we get:
f(0) = a(0)² + b(0) + c
f(0) = c
Therefοre, the value οf c in the standard fοrm οf the quadratic functiοn represents the number οf birds present οn the island when cοunting first started.
Sο, the fοrm that reveals the number οf birds present οn the island when cοunting first started is the standard fοrm. f(t) = at²+ bt + c
where c represents the initial number οf birds οn the island.
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Given the following exponential function identify whether the change represents growth or decay and determine the percentage rate of increase or decrease
y=8900(1.362)x
Answer:
Growth & 36.2%
Step-by-step explanation:
Exponential Growth Formula
A = A0 (1 + r)^t
A is the amount after certain number years
A0 is the initial amount
r is the rate
t is the number of years
Growth models are identified by the number between the parenthesis. If the number is greater than 1, then it represents a growth model. If the number is less than 1, then it represents a decay model.
To find the percentage by which it increases, you would simply convert the decimal. 1.362 becomes 36.2%. You move the decimal point two places to the right and add a percentage symbol next to it.
PLEASE HELPP
Linus wants to have 500 copies of his resume printed. His local print shop charges $18.50 for the first 200 copies and $9 for every 100 additional copies. How much will the 500 copies cost?
A)$46.25
B)$45.50
C)$45.00
D)$46.00
Question 4 of 10
The graph of F(x), shown below, resembles the graph of G(x)=x2, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
Answer: The answer is C, f(x) = 2x^2 + 3.
Step-by-step explanation: Check the graph below.
Mountain Trees Nursery has a great selection of trees for every yard. The nursery was busy last week delivering trees to local customers. The table below shows the number of trees that were transported in each delivery.
Number of trees Number of deliveries
1–2 2
3–4 3
5–6 4
7–8 2
9–10 1
Based on the data, estimate how many of the next 20 deliveries will transport more than 6 trees.
If necessary, round your answer to the nearest whole number.
What is the value of x that represents the solution to the equation below? 51x – 19.5 = 108
Answer:
2.5
Step-by-step explanation:
51x - 19.5 + 19.5 = 108 + 19.5
51x = 127.5
x = 127.5/51
= 2.5
A Christmas promotion included a $2.5 mail-in rebate for the purchase of a 10-liter bottle of milk and a store coupon for $1.39 off a 5-liter bottle of vegetable oil. Jesse Gatling bought one 10-liter bottle of milk for for $33.00 and a 5liter bottle of vegetables oil for $26.89. Calculate his total cost if an envelope costs $0.10 and a stamp costs $0.28
Answer:
can u break that down
Step-by-step explanation:
Please help I need these differential equations done by today and cannot do it.
the particular solution to the differential equation. we use the positive sign: [tex]y = -1 + e^(1/2 x^2 + x - 5.605)[/tex]
What is the differential equation?To find the particular solution to the differential equation {dy}/{dx} = (x+1) (y+1) with the initial condition y(4) = 3, we can use separation of variables and integration.
First, we can rewrite the equation as:
[tex]{1}/{(y+1)} dy = (x+1) dx[/tex]
Next, we can integrate both sides:
[tex]∫ {1}/{(y+1)} dy = ∫ (x+1) dx[/tex]
[tex]ln|y+1| = 1/2 x^2 + x + C[/tex]
where C is the constant of integration.
To determine the value of C, we can use the initial condition y(4) = 3:
[tex]ln|3+1| = 1/2 (4)^2 + 4 + C[/tex]
[tex]ln|4| = 10 + C[/tex]
[tex]C = ln|4| - 10 = -5.605[/tex]
Therefore, the particular solution to the differential equation with the initial condition y(4) = 3 is:
[tex]ln|y+1| = 1/2 x^2 + x - 5.605[/tex]
Solving for y:
[tex]|y+1| = e^(1/2 x^2 + x - 5.605)[/tex]
[tex]y+1 = \pm e^(1/2 x^2 + x - 5.605)[/tex]
[tex]y = -1 \pm e^(1/2 x^2 + x - 5.605)[/tex]
Since [tex]y(4) = 3[/tex], we can determine which sign to use:
[tex]3 = -1 + e^(1/2 (4)^2 + 4 - 5.605)[/tex]
[tex]3 = -1 + e^(7.395)[/tex]
[tex]4 = e^(7.395)[/tex]
Therefore, we use the positive sign: [tex]y = -1 + e^(1/2 x^2 + x - 5.605)[/tex]
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Jason goes to the sandwich shop for lunch. The prices for sandwiches are listed below.
What number completes the number sentence 3m = ?
2g
3g
4g
5g
The number completes the number sentence 3m= 5g.
What number completes the number sentence 3m = ?The m refers the meatball which prices $2.50
so for 3m = 3*2.50
3m = $7.5
g refers to grilled cheese which prices $1.50
so we have to find for how many grilled cheese which equals $7.5
On dividing we get, 7.5/1.50 = 5
Hence 3 meatballs equal 5 grilled cheese, 3m = 5g
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16^3 similar expressions
Answer: 2^12
4^6
64^2
the cube root of 4,096
256 times 2
8^6
65,536/4
16 times 16 times 16
256 cubed root of 256
256/16^4
64 times 4 times 2
Step-by-step explanation: All of these expressions are equal to 16 cubed, which is 4,096.
Answer:
4096 have a nice day
Step-by-step explanation:
pl z mark me brianliest :)
round to the nearest tenth 16 37 =x
The value of x in the given right triangle can be found with help of trigonometric-ratios, given an angle 16° and hypotenuse 37 units is 35.566657. On rounding off to nearest tenths we get 35.6 units.
What are trigonometric-ratios?
In a given right triangle, the ratios of different sides are represented as six trigonometric ratios which are cosine,sine,cosecant,cot,secant and tan.
Sin of an angle=[tex]\frac{side opposite to the angle}{hypotenuse of triangle}[/tex]
Cosine of an angle=[tex]\frac{side adjacent to the angle}{hypotenuse of the triangle}[/tex]
tan of an angle= [tex]\frac{side opposite to the angle}{side adjacent to the angle}[/tex]
And cosecant, secant and cot are the reciprocals of sine, cosine & tan respectively.
Here,on naming the given right triangle we can see that
∠A = 16° , AC=37 units and Side AB= x units
Applying cosine of angle 16°, we get
cos A=[tex]\frac{side adjacent to the angle}{hypotenuse of the triangle}[/tex]
Cos 16°=[tex]\frac{side adjacent to the angle}{hypotenuse of the triangle}[/tex]
Cos 16°= [tex]\frac{AB}{AC}[/tex]
0.961261= [tex]\frac{AB}{AC}[/tex] {Cos 16°=0.961261}
0.961261=[tex]\frac{x}{37}[/tex] {AB=x and AC=37}
x = 0.961261 (37)
x = 35.566657
On rounding off to nearest tenths x=35.6 units
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Refer to the attachment for complete question & naming of triangle.
3 Seventy-two books were to be divided up among 18 children. Which of the following expressions are equivalent to this fraction? Select THREE that apply. A. 8 6 B. }+ 8 D. 2•7 E. F. 3.
72 books were divided up among 18 children means 18 kids and 72 books equal 4 books for each youngster.
What is a fraction?An element of a whole is a portion. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a straightforward fraction. A fraction appears in the numerator or denominator of a complicated fraction. The numerator of a perfect fraction is less than the denominator.0
1) 8/3 split by 6/9: To begin, we divide both the numerator and denominator by 3 to reduce 6/9 to 2/3.
8/3 ÷ 2/3 = (8/3) x (3/2) = 4
The fraction we began with is not equivalent to this expression.
2) 8/3 times 2/3: By multiplying the numerators and denominators, we can reduce this expression:
(8/3) x (2/3) = 16/9
The fraction we began with is not equivalent to this expression.
3) 2/9 split by 8/9: We multiply the first fraction by the reciprocal of the second fraction to divide fractions:
(2/9) ÷ (8/9) = (2/9) x (9/8) = 1/4
The fraction we began with is not equivalent to this expression.
4) In order to simplify this equation, let's first reduce 8/2 to 4:
2 x 4 = 8
The fraction we began with is not equivalent to this expression.
The fraction that accurately describes the circumstance cannot be expressed using any of the given expressions.
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Number of Students
10
8
6
4
2
0
Test Scores for Ms. Gioia's Science Class
71-75 76-80 81-85 86-90 91-95 96-100
Science Test Scores
2) How many students in Ms. Gioia's class took the science test?
In the histogram , the number of students in Ms. Gioia's class took the science test is 27.
What is histogram?
A grouped frequency distribution with continuous classes is graphically represented by a histogram. It is an area diagram, and its size is proportional to the frequencies in the associated classes. Due to the base's coverage of the spaces between class boundaries, all of the rectangles in such representations are contiguous.
Here according to the histogram ,
The number of students score between 71-75 = 4
The number of students score between 76-80 = 6
The number of students score between 86-90 =8
The number of students score between 91-95 = 7
The number of student score between 96-100 = 2
Then number of students in Ms. Gioia's class took the science test is,
=> 4+6+8+7+2 = 27
Hence the number of students in Ms. Gioia's class took the science test is 27.
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a national survey reported that 35% of adults in a certain country have hypertension a sample of 25 adults is studied what is the mean number of adults who have hypertension
The mean number of adults who have hypertension in a sample of 25 adults is 8.75, assuming the national survey-reported percentage of adults with hypertension (35%) applies to the sample.
The mean number of adults who have hypertension in the sample of 25 can be calculated by multiplying the sample size (25) by the population proportion (0.35). Mathematically,
Mean = n * p = 25 * 0.35 = 8.75
Therefore, the mean number of adults who have hypertension in the sample is 8.75. Note that this is an expected value and there may be variability around this mean in different samples.
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b. Use function notation to write a rule
that defines function r.
c. On the coordinate plane, sketch a
graph of function r.
d. Solve the equation r(u) = 30 and
explain what the solution means in
this situation.
Using functions,
a) 1. 48
2. 21
3. 75 - 4.5w
b) r = 75 - 4.5w
c) Graph is attached.
d) The restaurant has 30kgs of rice after 10 weeks.
Define a function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Here as per the question,
a)
1. 75 - (4.5 × 6)
= 75 - 27
= 48
2. 75 - (4.5 × 12)
= 75 - 54
= 21
3. 75 - (4.5 × w)
= 75 - 4.5w
b)
r = 75 - 4.5w
c) Image is attached for the graph.
d) 30 = 75 - 4.5w
Subtracting both sides by 30:
⇒ 0 = 75 - 4.5w - 30
Adding both sides by 4.5w:
⇒ 4.5w = 75 - 30
⇒ 4.5w = 45
Dividing both sides by 4.5:
⇒ w = 45/4.5
⇒ w = 10.
Therefore, the restaurant has 30kgs of rice after 10 weeks.
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The complete question is:
b. Use function notation to write a rule
that defines function r.
c. On the coordinate plane, sketch a
graph of function r.
d. Solve the equation r(u) = 30 and
explain what the solution means in
this situation.
Help meeeeeeee pleaseee
a. Mason's error is that he flipped the inequality sign. The correct solution is x > 6.
b. This indicates that any value of x greater than 6 (but not equal to 6) will satisfy the inequality x > 6.
What is inequality?An inequality is a mathematical statement that compares two values or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to). Inequalities can be used to describe a range of values that a variable can take, rather than just a single value.
a. Mason's error is that he flipped the inequality sign. The correct solution is x > 6.
b. To show the correct solution on the number line, we start by marking 6 on the number line with an open circle (since x is not equal to 6). Then, we shade the area to the right of 6, because x is greater than 6. The graph should look like this:
0 1 2 3 4 5 6o 7 8 9
--------
shaded
This indicates that any value of x greater than 6 (but not equal to 6) will satisfy the inequality x > 6.
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4. if an athlete eats a large meal before a competition, how many hours before the competition should she finish eating? a. 1 hour b. 1.5 hours c. 2 hours d. 2.5 hours e. 3 hours
Option D is the correct option i.e., 2.5 hours. Timing is everything when it comes to dining before a fight. Athletes must ingest enough calories to power their efforts without developing gastrointestinal pain or bloating while competing. Typically, a substantial dinner should be eaten two to three hours prior to the game.
The body needs time to process and assimilate nutrients, which is the cause of this. A big dinner requires the body to divert a lot of blood flow to the digestive system, which can have an impact on an athlete's performance. Athletes' performance can be hampered by sluggishness, gastrointestinal pain, or even vomiting brought on by eating too close to a competition.
In general, it is recommended that athletes experiment with different meal timings and types of food during their training to determine what works best for their individual needs.
They should also consider the length of the event and the intensity of their activity to determine the amount and timing of their meals. A registered dietitian or sports nutritionist can help athletes create a personalized nutrition plan to optimize their performance.
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a car manufacturer claims that its new hybrid car can travel at speeds more than 60 mpg. the actual mpg is approximately normally distributed with a mean of 52 miles and a standard deviation of three miles. what is the probability that the manufacturer's claim is valid?
The probability that the manufacturer's claim is valid is 0.0037, or 0.37%.
The student question asks about the probability that the car manufacturer's claim of the hybrid car traveling at speeds more than 60 mpg is valid. The actual mpg is approximately normally distributed with a mean of 52 miles and a standard deviation of three miles.
To calculate the probability, we will use the Z-score formula:
Z = (X - μ) / σ
Where:
Z is the Z-score
X is the value we want to find the probability for (in this case, 60 mpg)
μ is the mean (52 miles)
σ is the standard deviation (3 miles)
Plug in the values into the Z-score formula:
Z = (60 - 52) / 3
Calculate the Z-score:
Z = 8 / 3 ≈ 2.67
Now we have the Z-score of 2.67, which tells us how many standard deviations above the mean the value of 60 mpg is. The next step is to use a Z-table (also known as the standard normal table) to find the probability.
Look up the Z-score in the Z-table:
For a Z-score of 2.67, the corresponding probability in the Z-table is 0.9963.
This means that 99.63% of the data falls below 60 mpg.
Find the probability that the claim is valid:
Since we want to find the probability that the car travels at speeds more than 60 mpg, we need to find the area to the right of the Z-score in the normal distribution curve. To do this, we subtract the probability from 1
Probability = 1 - 0.9963 = 0.0037
The probability that the manufacturer's claim is valid is 0.0037, or 0.37%.
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Find the area of the composite figure
Answer:
186 inches
Step-by-step explanation:
8×6=48
5.5×16=88
10×5=50
48+88+50=186
in the last 10 softball games delisa has scored the following number of runs for her team: 2, 1, 3, 3, 1, 3, 2, 4, 3, 5. the mode number of runs for delisa would be:
In the last 10 softball games, the mode number of runs for Delisa is 3.
Mode is the value that appears most frequently in a given data set. It is one of the three measures of central tendency, along with mean and median.
To find the mode, we need to determine which number appears most frequently in the data set. In this case, the number of runs that Delisa scored in each game.
We have been given the data points,
2,1,3,3,1,3,2,4,3,5
The number 3 appears most frequently, occurring three times. Therefore, the mode number of runs for Delisa is 3.
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Solve the following question
3to the power 2x multiplied by 9 to the power y =243 .
Solve for x and y
Solving the statement, we get the equation x=2.5-y
Define exponentsExponents are a mathematical notation used to represent repeated multiplication of a number by itself. Exponents are written as a superscript to the right of the base number, which is the number being multiplied.
given equation:
3²ˣ × [tex]9^{y}[/tex] = 243
Simplifying the expression on the right-hand side, we get:
3²ˣ × [tex]9^{y}[/tex] = 3⁵
Using the property of exponents that states that when multiplying powers with the same base, we can add their exponents, we get:
[tex]3^{2x+2y}[/tex] = 3⁵
For the equation to hold, the exponents on both sides must be equal. Therefore:
2x + 2y = 5
Dividing both sides by 2, we get:
x + y = 2.5
x=2.5-y
Hence, solving the statement, we get the equation x=2.5-y
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If <1 and <2 are vertical angles and m<22 = 180°, find m<1
If ∠1 and ∠2 are vertical angles and m∠22 = 180°, then m∠1 = 90°
Vertical angles are pairs of angles that are opposite to each other when two lines intersect. Vertical angles are always equal in measure. Therefore, if ∠1 and ∠2 are vertical angles, then:
∠1 = ∠2
We are also given that m∠22 has a measure of 180°. Since ∠1 and ∠2 are vertical angles, they form a straight line, and their measures add up to 180°. Therefore:
∠1 + ∠2 = 180°
Since ∠1 = ∠2, we can substitute ∠1 for ∠2 in the above equation:
∠1 + ∠1 = 180°
Simplifying the equation, we get:
2∠1 = 180°
Dividing both sides by 2, we get:
∠1 = 90°
Therefore, ∠1 has a measure of 90°.
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what reflection occurred? Explain please.
The reflection that occurred is over the x-axis.
EquationsBased on the given coordinates, it can be observed that each point of the pre-image was reflected over the x-axis, resulting in a new image. Therefore, the type of reflection that occurred is a reflection over the x-axis.
To explain this with equations, we can use the transformation formula for a reflection over the x-axis:
(x, y) → (x, -y)
Using this formula, we can find the image coordinates of the pre-image points:
A' = (-1, -8)
B' = (5, 3)
C' = (-5, 1)
As we can see, the y-coordinates of each point have been negated, indicating a reflection over the x-axis. Therefore, the type of reflection that occurred is a reflection over the x-axis.
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