Answer:
Sure, I can help you with that! First, we know that the vertex form of a quadratic function is: f(x) = a(x - h)^2 + k where (h, k) is the vertex of the parabola. So we can plug in the values we have: f(x) = a(x - 2)^2 + 1 Now we just need to find the value of "a". To do that, we can use the fact that the function goes through the point (4, 5). So we can plug in those values: 5 = a(4 - 2)^2 + 1 Simplifying, we get: 5 = 4a + 1 4a = 4 a = 1 So now we know that the quadratic function is: f(x) = (
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
To know more about powers, visit:
https://brainly.com/question/30150415
#SPJ1
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
To know more about trigonometric-ratios, visit:
https://brainly.com/question/1201366
#SPJ1
Refer to the attachment for complete question & naming of triangle.
Helppp !!! Giving 20 pts !!
To determine when the ball strikes the ground, we need to find the value of t when the height h(t) is 0.
The equation for the ball's height h at time t seconds after launch is:
h(t) = -4.9t^2 + 9.31t + 239.12
Setting h(t) to 0, we get:
0 = -4.9t^2 + 9.31t + 239.12
We can solve this quadratic equation using the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -4.9, b = 9.31, and c = 239.12.
Answer: 6.12 seconds
Step-by-step explanation:
To find when the object strikes the ground, we need to find the time t when the height h(t) is equal to 0 (since the ground is at height 0). We have the equation:
h(t) = -4.9t² + 9.31t + 239.12
To find the time when the object strikes the ground, we need to find the value of t when h(t) = 0:
0 = -4.9t² + 9.31t + 239.12
This is a quadratic equation of the form at² + bt + c = 0, where a = -4.9, b = 9.31, and c = 239.12. We can solve this equation for t using the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
Plugging the values of a, b, and c into the formula, we get:
t = (-(9.31) ± √((9.31)² - 4(-4.9)(239.12))) / (2(-4.9))
t = (-9.31 ± √(86.6161 + 4694.336)) / (-9.8)
t = (-9.31 ± √(4780.9521)) / (-9.8)
t ≈ (-9.31 ± 69.14) / (-9.8)
We will have two possible values for t:
t₁ ≈ (-9.31 + 69.14) / (-9.8) ≈ 6.12 (rounded to two decimal places)
t₂ ≈ (-9.31 - 69.14) / (-9.8) ≈ 8.00 (rounded to two decimal places)
Since the height function describes the motion of the ball from a platform, we can discard the negative solution as it represents an invalid time before the ball is launched. Thus, the object strikes the ground at approximately t ≈ 6.12 seconds.
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.
To learn more about distance visit:
https://brainly.com/question/17273444
#SPJ1
Complete question:
Find the distance between point (15,-17) and (-20,-5).
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.
To know more about functions, visit:
https://brainly.com/question/12431044
#SPJ9
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.
Determine whether the triangles are similar, If similar state how( AA. SSS. SAS) and write a similarity statement.
By the AA similarity theorem, we can conclude that triangles FGH and FPQ are similar.
EquationsTo prove that triangles FGH and FPQ are similar, we need to show that their corresponding angles are congruent and their corresponding sides are proportional.
Angle F in triangle FGH corresponds to angle F in triangle FPQ
Angle H in triangle FGH corresponds to angle Q in triangle FPQ
Angle G in triangle FGH corresponds to angle P in triangle FPQ
From the problem, we know that angle F = 63 degrees and angle H = 30 degrees. We also know that angle GPQ = 93 degrees, which means angle G + angle P = 93 degrees. Therefore, angle G = 93 degrees - angle P
Using the fact that the sum of angles in a triangle is 180 degrees, we can find angle Q:
Angle FGH: angle F + angle G + angle H = 63 degrees + (93 - angle P) + 30 degrees = 186 - angle P degrees
Triangle FPQ: angle F + angle P + angle Q = 180 degrees
Therefore, angle Q = 180 - angle F - angle P = 117 - angle P degrees
Now, we can compare the corresponding sides:
Side FG in triangle FGH corresponds to side FQ in triangle FPQ
Side GH in triangle FGH corresponds to side PQ in triangle FPQ
Side FH in triangle FGH corresponds to side PQ in triangle FPQ
To show that these sides are proportional, we can use the Angle-Angle (AA) similarity theorem and We already know that angle F in triangle FGH corresponds to angle F in triangle FPQ, and angle G in triangle FGH corresponds to angle P in triangle FPQ. We just showed that angle Q in triangle FPQ corresponds to angle H in triangle FGH. Therefore, we have two pairs of corresponding angles that are congruent.
To know more about Similar Triangles, click here,
https://brainly.com/question/14926756
#SPJ1
125 invitations to 75 invitations
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.
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.
york steel corporation produces a special bearing that must meet rigid specifications. when the production process is running properly, 10% of the bearings fail to meet the required specifications. sometimes problems develop with the production process that cause the rejection rate to exceed 10%. to guard against this higher rejection rate, samples of 15 bearings are taken periodically and carefully inspected. if more than 2 bearings in a sample of 15 fail to meet the required specifications, production is suspended for necessary adjustments. a . a.if the true rate of rejection is 10% (that is, the production process is working properly), what is the probability that the production will be suspended based on a sample of 15 bearings? b . b.what assumptions did you make in part a?
a) If the true rate of rejection is 10%, then the probability that the production will be suspended based on a sample of 15 bearings is 10%.
b) The assumptions made in part a are that the sample of 15 bearings is representative of the population of bearings produced, and that each bearing is independent of the others.
To ensure that the production process is producing quality products, samples of 15 bearings are taken periodically and carefully inspected. If more than 2 bearings in a sample of 15 fail to meet the required specifications, production is suspended for necessary adjustments.
a) If the true rate of rejection is 10%, what is the probability that the production will be suspended based on a sample of 15 bearings? To answer this question, we need to use the binomial distribution. The binomial distribution is used to calculate the probability of a certain number of successes in a fixed number of independent trials. In this case, the number of trials is 15, and the probability of success (i.e., a bearing not meeting the required specifications) is 10%.
b) The assumptions allow us to use the binomial distribution to calculate the probability of having a certain number of bearings fail to meet the required specifications in a sample of 15. Additionally, we assume that the true rate of rejection is 10%, which may not always be the case.
To know more about probability here
https://brainly.com/question/11234923
#SPJ4
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.
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.
To know more about inequality visit:
brainly.com/question/29914203
#SPJ1
i need help quickly 40j-16
Answer:
Answer: 40j - 16 = 40j + (-16) (Additive inverse property) = 40j + (-1)(16) (Distributive property) = 40j + (-1)(4)2 (FOIL - first, outer, inner, last) = (40j + (-1)4) + (-1)2 (Order of operations - parentheses first) = (40j - 4) + (-1)2 (Distributive property) = 36j - 2
Answer:
8(5j−2)
Step-by-step explanation:
1 / 4
Let's find the greatest common factor of 40
8 is greatest common factor
40j/8 - 16/8
=
8(5j-2)
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
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.
Learn more about arithmetic expression here:
https://brainly.com/question/17722547
#SPJ1
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 :)
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.
To know more about mean:
https://brainly.com/question/21800892
#SPJ4
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.
To know more about quadratic equation visit,
https://brainly.com/question/1214333
#SPJ9
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.
To learn more about histogram refer the below link
https://brainly.com/question/2962546
#SPJ9
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.
To learn more about : problem
https://brainly.com/question/31006424
#SPJ11
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.
To know more about reflection of a point, click here,
https://brainly.com/question/1548989
#SPJ1
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%.
For similar questions on probability:
https://brainly.in/question/23094285
#SPJ11
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
If jose used 4 gallons of wood sealant to cover the hemispherical ceiling of his vacation home, how many gallons of wood sealant are needed to cover the floor?
4/3 Gallons of wood sealant are needed to cover the floor of Jose's vacation home.
To determine how many gallons of wood sealant are needed to cover the floor, first, we need to find the relationship
between the surface area of the hemispherical ceiling and the floor.
Calculate the surface area of the hemispherical ceiling.
The surface area of a hemisphere is given by the formula [tex]3πr^2[/tex], where r is the radius.
Calculate the surface area of the floor.
The floor is a circle, so its surface area is given by the formula[tex]πr^2[/tex].
Determine the ratio between the surface areas.
Divide the surface area of the floor by the surface area of the hemispherical ceiling: [tex](πr^2) / (3πr^2).[/tex] The [tex]πr^2[/tex]terms
cancel out, leaving 1/3.
Apply the ratio to the amount of wood sealant used for the ceiling.
Since Jose used 4 gallons of wood sealant for the ceiling, we can multiply this by the ratio to find the amount needed
for the floor: 4 gallons × (1/3) = 4/3 gallons.
Therefore, 4/3 gallons of wood sealant are needed to cover the floor of Jose's vacation home.
for such more question on surface area
https://brainly.com/question/27987869
#SPJ11
canadian radio stations are required to have at least 35% of their content be canadian in origin. a listener sampled his favorite station's content to test whether it is falling short of the quota. in his sample of 100 time intervals, canadian content was playing for 33 of them. what is the test statistic for this test?
The test statistic for this hypothesis test is -0.3886.
In statistical hypothesis testing, a test statistic is a numerical value that is calculated from a sample of data and used to determine whether to accept or reject the null hypothesis.
To calculate the test statistic for this hypothesis test, we need to use the formula for the proportion test
z = (p - P) / sqrt(P(1-P) / n)
Where
p is the proportion of Canadian content in the sample (33/100 = 0.33)
P is the hypothesized proportion (35% = 0.35)
n is the sample size (100)
Substituting the values, we get
z = (0.33 - 0.35) / sqrt(0.35(1-0.35) / 100)
z = -0.02 / 0.0516
z = -0.3886
Learn more about test statistic here
brainly.com/question/28068076
#SPJ4
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.
To know more about Coffee Haven visit:
https://brainly.com/question/28381366
#SPJ1
Help I needed please
Answer:
Step-by-step explanation:
Area = length x height
A = 2.4 x 5.6
A = 13.44 in^2
Pls help and explain♀️
the equation that relates the time it took James to sort the supplies for b bags is: t = 1.5b
option D.
What is the equation?Sherry sorted enough supplies for 10 bags in 30 minutes (from 10:10 a.m. to 10:40 a.m.). Let's call the rate at which Sherry sorted the supplies "r."
Then, we can write:
r = 10 bags / 30 minutes
r = 1/3 bags per minute
Since James sorted twice as fast as Sherry, his rate is 2r:
2r = 2/3 bags per minute
To find the time it took James to sort b bags, we can use the formula:
time = (amount of work) / (rate of work)
In this case, the "amount of work" is b bags, and the "rate of work" is 2/3 bags per minute. So, we get:
time = b / (2/3)
time = (3/2) b
Therefore, the equation that relates the time it took James to sort the supplies for b bags is:
t = (3/2) b
So, the correct answer is (D) t = 1.5b.
Learn more about equations here: https://brainly.com/question/2972832
#SPJ1
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.
Know more about the proportion of numbers
https://brainly.com/question/1496357
#SPJ1