we can be 98% confident that the true mean weight of pretzel bags produced by the manufacturer lies between 12.47 and 12.93 ounces.
To finder lies between produce by the 98% confidence interval of the true mean, we can use the formula:
CI = x ± z* (σ/√n)
where x is the sample mean, σ is the population standard deviation (which we don't know), n is the sample size, and z* is the z-score corresponding to the desired level of confidence (98% in this case).
Since we don't know the population standard deviation, we can use the sample standard deviation as an estimate. The z-score corresponding to 98% confidence level is 2.33 (from the standard normal distribution table). Thus, the 98% confidence interval for the true mean is:
CI = 12.7 ± 2.33 * (0.60/√41)
CI = 12.7 ± 0.23
CI = (12.47, 12.93)
Therefore, wewe can be 98% confident that the true mean weight of pretzel bags produced by the manufacturer lies between 12.47 and 12.93 ounces.
to learn more about population click here:brainly.com/question/31598322
#SPJ11
What is the sign of 3 5 + 3 5 5 3 + 5 3 start fraction, 3, divided by, 5, end fraction, plus, start fraction, 3, divided by, 5, end fraction? Choose 1 answer:
The sign of the expression can be determined by examining the signs of the individual terms involved.
3/5: The sign of this term depends on the sign of the numerator (3) and the denominator (5). As both the numerator and denominator are positive, this term is positive.
(3/5) / (5/3): To simplify this expression, we can multiply the numerator and denominator of the second fraction by 3/5, resulting in (3/5) * (3/5) / 1. The numerator is positive as it is the product of two positive numbers, and the denominator is positive as well. Therefore, this term is positive.
Combining the two positive terms, the overall expression will have a positive sign.
Know more about expression here:
https://brainly.com/question/14083225
#SPJ11
The variables x and y vary directly, and y =
24 when x = 4. Write the equation that
relates x and y.
A)y=6x
B)y=96x
C)y=6/y
D)y=96/x
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies directly with "x"}}{y = k(x)}\hspace{5em}\textit{we also know that} \begin{cases} y=24\\ x=4 \end{cases} \\\\\\ 24=k(4)\implies \cfrac{24}{4}=k\implies 6=k\hspace{9em}\boxed{y=6x}[/tex]
a force is applied tyo a 2kg radio controlled model car parallel to the x axis as it moves along a straight track. The x-component of the forces varies with the x-coordinate of the car as shown in the figure.
no title provided
Calculate the work done by the force F when the car moves from x=4.0m to x=7.0m.
W=___J
Calculate the work done by the force F when the car moves from x=0 to x=7.0m.
W=___J
Calculate the work done by the force F when the car moves from x=7.0m to x=2.0m
W=___J
Therefore, According to the given information: W = 30 J (x=4.0m to x=7.0m), W = 40 J (x=0 to x=7.0m and x=7.0m to x=2.0m)
To calculate work, we use the formula W = F * d * cos(theta), where F is the force applied, d is the distance moved, and theta is the angle between the force and displacement vectors. Since the force is parallel to the x-axis, theta = 0 and cos(theta) = 1.
For the first question, the force is constant between x=4.0m and x=7.0m, so we can use W = F * d = (10 N)(3.0 m) = 30 J.
For the second question, we need to split the distance into segments where the force is constant. From x=0 to x=2.0m, the force is 0 N, so no work is done. From x=2.0m to x=4.0m, the force is 5 N, so W = (5 N)(2.0 m) = 10 J. From x=4.0m to x=7.0m, the force is 10 N, so W = (10 N)(3.0 m) = 30 J. Adding these up gives W = 40 J.
For the third question, we use the same approach as the second question but in reverse. From x=7.0m to x=4.0m, the force is 10 N, so W = (10 N)(3.0 m) = 30 J. From x=4.0m to x=2.0m, the force is 5 N, so W = (5 N)(2.0 m) = 10 J. From x=2.0m to x=0, the force is 0 N, so no work is done. Adding these up gives W = 40 J.
Therefore, According to the given information: W = 30 J (x=4.0m to x=7.0m), W = 40 J (x=0 to x=7.0m and x=7.0m to x=2.0m)
To know more about equations visit:
https://brainly.com/question/22688504
#SPJ11
Three ladies watches cost as much as five dresses. If the average cost of 5 watches and 3 dresses is $148. 75, what is the cost of six dresses?
The cost of six dresses is $145.74.
Let's assign variables to represent the costs of the watches and dresses. Let w be the cost of one watch, and d be the cost of one dress.
From the given information, we can set up the following equations:
3w = 5d (Three ladies watches cost as much as five dresses)
(5w + 3d) / 8 = $148.75 (Average cost of 5 watches and 3 dresses is $148.75)
From the first equation, we can solve for w in terms of d:
w = (5d) / 3
Substituting this expression for w into the second equation, we can solve for d:
(5[(5d) / 3] + 3d) / 8 = $148.75
Simplifying the equation:
(25d + 24d) / 24 = $148.75 * 8
49d = $1190
Dividing both sides by 49, we find:
d = $24.29
The cost of six dresses would be:
6 * $24.29 = $145.74
Know more about cost here:
https://brainly.com/question/30045916
#SPJ11
give the total number of isomers with the formula [pd(c2o4)2i2]2–.
The total number of isomers with the formula [Pd(C2O4)2I2]2– is 3150.
There are two parts to this answer: the first part is to determine the coordination number of the central palladium (Pd) atom, and the second part is to determine the number of possible isomers based on the coordination number.
To determine the coordination number, we need to count the number of ligands (the molecules that bind to the central atom) attached to the Pd atom. In this case, we have four oxalate (C2O4) ligands, each of which contributes two atoms (a total of eight atoms), and two iodide (I) ligands, each of which contributes one atom (a total of two atoms). This gives us a total of 10 ligands attached to the Pd atom. Since each ligand can only form one bond with the Pd atom, the coordination number is 10.
Next, we need to determine the number of possible isomers. Isomers are molecules with the same chemical formula but different arrangements of atoms. For this complex ion, there are two types of isomers: geometrical and optical.
Geometrical isomers arise from the fact that the ligands can be arranged around the central atom in different ways. In this case, since there are 10 ligands, there are a total of 10!/[(4!2!2!)x2] possible geometrical isomers, or 3150.
Optical isomers arise when there are non-superimposable mirror images of the molecule. However, since this complex ion has a plane of symmetry, it is achiral and does not have optical isomers.
Therefore, the total number of isomers with the formula [Pd(C2O4)2I2]2– is 3150.
Learn more about central palladium (Pd)
brainly.com/question/14698291
#SPJ11
The guests are 500 people if the drinks charge $4, and the cookie is $2. for every 5 drinks sold, the shop expects to sell 3 cookies. what is the revenue?
The total revenue is $2600.
To calculate the revenue, we need to determine the total number of drinks and cookies sold and multiply them by their respective prices.
Number of drinks sold: 500 people
Number of cookies sold (assuming for every 5 drinks, 3 cookies are sold): (500 / 5) * 3 = 300 cookies
Price per drink: $4
Price per cookie: $2
Total revenue from drinks: Number of drinks sold * Price per drink = 500 * $4 = $2000
Total revenue from cookies: Number of cookies sold * Price per cookie = 300 * $2 = $600
Total revenue = Revenue from drinks + Revenue from cookies = $2000 + $600 = $2600
Know more about revenue here:
https://brainly.com/question/31683012
#SPJ11
Urgent, please help! I’ll give 5 stars if answering.
Geometry - Area with similar quadrilaterals
Answer:
637 cm²
Step-by-step explanation:
You want the area of the larger of two similar pentagons, given that the area of the smaller is 13 cm². Corresponding side lengths are in the ratio 14 : 2.
Scale factorThe (14 cm) : (2 cm) ratio of corresponding sides in the two figures tells you the scale factor is 14/2 = 7. The area of the larger pentagon will be the area of the smaller, multiplied by the square of this scale factor:
(13 cm²)×7² = 637 cm²
The area of pentagon S is 637 cm².
<95141404393>
Need the answer to this using SOH-CAH-TOA
Answer:
[tex]x \approx 16.26\°[/tex]
Step-by-step explanation:
We can solve for angle x in this right triangle using the trigonometric ratio sine.
[tex]\sin(\theta) = \dfrac{\text{opposite}}{\text{hypotenuse}}[/tex] ... This is the SOH part of SOH-CAH-TOA
↓ plugging in the given values
[tex]\sin(x) = \dfrac{7}{25}[/tex]
↓ taking the inverse sine of both sides
[tex]\sin^{-1}(\sin(x)) = \sin^{-1}\left(\dfrac{7}{25}\right)[/tex]
↓ canceling ... [tex]\sin^{-1}(\sin(\theta)) = \theta[/tex]
[tex]x = \sin^{-1}\left(\dfrac{7}{25}\right)[/tex]
↓ plugging into a calculator
[tex]\boxed{x \approx 16.26\°}[/tex]
What are the x-intercepts of the parabola? (1 point)
graph of parabola falling from the left, passing through negative 6 comma 2 to about negative 4 and one half comma negative one fourth, and rising to the right, passing through negative 3 comma 2
Answer:
x = -5 and x = -4 are the x-intercepts of this parabola.
Let y=[-3 5 0 -4] , v1= [3 -4 2 -1] , v2= [-4 1 -2 -20]. Compute the distance d from y to the subspace of R4 spanned by v1 and v2. d=
To find the distance d from y to the subspace of R4 spanned by v1 and v2, we can use the formula. The distance d from y to the subspace of R4 spanned by v1 and v2 is approximately 6.558.
d = ||y - proj_v(y)||
where proj_v(y) is the projection of y onto the subspace spanned by v1 and v2. We can find proj_v(y) as:
proj_v(y) = ((y · v1)/(v1 · v1)) v1 + ((y · v2)/(v2 · v2)) v2
where · represents the dot product. Plugging in the given values, we get:
proj_v(y) = ((-3)(3) + (5)(-4) + (0)(2) + (-4)(-1))/(3^2 + (-4)^2 + 2^2 + (-1)^2) [3 -4 2 -1] + ((-3)(-4) + (5)(1) + (0)(-2) + (-4)(-20))/((-4)^2 + 1^2 + (-2)^2 + (-20)^2) [-4 1 -2 -20]
= (-26/30) [3 -4 2 -1] + (53/441) [-4 1 -2 -20]
= [-34/35 77/210 -43/105 -617/441]
Then, we can calculate the distance d as:
d = ||y - proj_v(y)|| = ||[-3 5 0 -4] - [-34/35 77/210 -43/105 -617/441]|| = ||[77/35 -131/210 43/105 -1117/441]||
= sqrt((77/35)^2 + (-131/210)^2 + (43/105)^2 + (-1117/441)^2)
= 6.558
Therefore, the distance d from y to the subspace of R4 spanned by v1 and v2 is approximately 6.558.
To compute the distance d from y to the subspace of R4 spanned by v1 and v2, we first need to find the orthogonal projection of y onto the subspace. Let's denote the projection as p(y).
1. Find the coordinates of y with respect to the basis {v1, v2}. Solve the equation: c1 * v1 + c2 * v2 = y.
2. Calculate p(y) using the coordinates found in step 1: p(y) = c1 * v1 + c2 * v2.
3. Calculate the distance d using the formula d = ||y - p(y)||.
After following these steps, you will find the distance d from y to the subspace of R4 spanned by v1 and v2.
Learn more about distance at: brainly.com/question/15172156
#SPJ11
fill in the blank. the binary number 0000 1010 can be expressed as in hexadecimal.
The binary number 0000 1010 can be expressed as 0A in hexadecimal. Hexadecimal is a base-16 numbering system that uses 16 digits, where 0-9 represent their respective values and A-F represents values 10-15, respectively.
To convert binary to hexadecimal, the binary number is grouped into four bits, starting from the right side, and each group is converted to its equivalent hexadecimal digit. In this case, the binary number 0000 1010 has two groups, 0000 and 1010. The first group is equal to 0 in hexadecimal, and the second group is equal to A in hexadecimal. Therefore, the binary number 0000 1010 can be expressed as 0A in hexadecimal. It is important to note that hexadecimal is often used in computer programming, as it is a convenient way to represent binary data.
To learn more about hexadecimal, refer:-
https://brainly.com/question/28875438
#SPJ11
using the information in question 33, what is the probability that a random chosen testtaker will score between 400 to 550 (round your answer to four decimal places)
Answer: The probability that a random chosen test taker will score between 400 and 550 is approximately 0.5328.
Step-by-step explanation:
From question 33, we know that the mean score is 500 and the standard deviation is 100.
To obtain the probability that a random test taker will score between 400 and 550, we need to standardise these scores using the formula:
z = (x - μ) / σ
where x is the score we are interested in, μ is the mean score, and σ is the standard deviation.
For x = 400:
z = (400 - 500) / 100 = -1
For x = 550:
z = (550 - 500) / 100 = 0.5
Using a standard normal distribution table or calculator, we can find the probability of z being between -1 and 0.5:
P(-1 < z < 0.5) = P(z < 0.5) - P(z < -1)
= 0.6915 - 0.1587
= 0.5328
Therefore, the probability that a random chosen test taker will score between 400 and 550 is approximately 0.5328.
Learn more about probability here, https://brainly.com/question/25839839
#SPJ11
Given the vector \mathbf{u}u equal to 7\left<\cos 0^{\circ},\,\sin 0^{\circ}\right>7⟨cos0
∘
,sin0
∘
⟩ and vector \mathbf{v}v equal to 4\left<\cos 135^{\circ},\,\sin 135^{\circ}\right>,4⟨cos135
∘
,sin135
∘
⟩, find the sum \mathbf{u}+\mathbf{v}u+v and write your answer in magnitude and direction form with the magnitude rounded to the nearest tenth and the direction rounded to the nearest degree, 0^{\circ}\le \theta < 360^{\circ}. 0
∘
≤θ<360
∘
The vector sum [tex]\mathbf{u}+\mathbf{v}[/tex] is approximately equal to [tex]3.9\left < \cos 26^{\circ},,\sin 26^{\circ}\right > , 3.9⟨cos26∘, sin26∘⟩[/tex] in magnitude and direction form.
To find the sum of two vectors, we add their corresponding components. In this case, [tex]\mathbf{u}+\mathbf{v} = 7\left < \cos 0^{\circ},,\sin 0^{\circ}\right > + 4\left < \cos 135^{\circ},,\sin 135^{\circ}\right >[/tex]. Evaluating the x- and y-components separately, we get:
[tex]\mathbf{u}+\mathbf{v} = (7\cos 0^{\circ} + 4\cos 135^{\circ}),\mathbf{i} + (7\sin 0^{\circ} + 4\sin 135^{\circ}),\mathbf{j}[/tex]
[tex]\mathbf{u}+\mathbf{v} = 3.9,\left < \cos 26^{\circ},,\sin 26^{\circ}\right >[/tex]
To write the answer in magnitude and direction form, we can use the ormula [tex]\left|\mathbf{u}+\mathbf{v}\right| = \sqrt{(u_1+v_1)^2 + (u_2+v_2)^2}[/tex] for the magnitude, and [tex]\theta = \tan^{-1}\left(\frac{u_2+v_2}{u_1+v_1}\right)[/tex] for the direction. Plugging in the values, we get:
[tex]\left|\mathbf{u}+\mathbf{v}\right| \approx 3.9\theta \approx 26^{\circ}[/tex]
Therefore, the vector sum [tex]\mathbf{u}+\mathbf{v} is approximately equal to 3.9\left < \cos 26^{\circ},,\sin 26^{\circ}\right > , 3.9⟨cos26∘, sin26∘⟩[/tex] in magnitude and direction form.
Learn more about magnitude here
https://brainly.com/question/30337362
#SPJ11
7. Calculate Turnover tax (TOT) on sales of Birr 25,000.
Hurry pls
The VAT for the year is Birr 75,600.
Here, we have,
The pharmacy makes 42,000 Birr in monthly sales, as stated in the problem.
We must divide the monthly sales by the number of months in a year in order to determine the overall annual sales:
Total annual sales are calculated as follows: Birr 42,000 multiplied by 12 months to equal Birr 504,000.
Now that we have the VAT rate that is in effect in the area where the pharmacy is located, we can calculate the VAT (Value Added Tax). The VAT is often calculated as a share of sales.
Assuming a 15% VAT rate, the VAT can be calculated as follows:
VAT = 15% of total annual sales, which equals 0.15 times Birr 504,000 ($75,600).
Therefore, the VAT for the entire year is 75,600 Birr.
Learn more about VAT , here:
brainly.com/question/31341634
#SPJ1
complete question:
Jessica pharmacy has monthly sales of Birr 42,000. If the pharmacy is open for a year , calculate TOT or VAT???
is it wise to use the correlation coefficient r to summerize the association between this new pair of variables? why or why not?
It is not wise to use the correlation coefficient r to summarize the association between this new pair of variables, without first examining the data and considering the context of the problem.
The correlation coefficient r measures the strength and direction of the linear relationship between two variables. However, it assumes that the relationship between the variables is linear, and that there are no outliers or influential points that could affect the results.
If the relationship between the variables is not linear or there are outliers, then the correlation coefficient r may not accurately summarize the association between the variables. In this case, it would be more appropriate to use other measures, such as nonparametric correlation coefficients or regression analysis.
Therefore, before using the correlation coefficient r, it is important to carefully examine the data and consider any potential issues that could affect the results. Only then can we determine whether the correlation coefficient r is an appropriate measure for summarizing the association between the variables.
To learn more about nonparametric click here, brainly.com/question/30928348
#SPJ11
The demand equation for a product is p = 29 -0.01q
Write the revenue as a function of q and find the qunatity that maximizes revenue
R(q) =
The quantity that maximizes revenue is _____________________
The price of each item at this production level is $________________
The total revenue at this price is $_______________________
The quantity that maximizes revenue is 1450.
The price of each item at this production level is $14.50.
The total revenue at this price is $21,025.
The revenue as a function of q can be found by multiplying the price (p) by the quantity (q):
R(q) = pq = q(29 - 0.01q) = 29q - 0.01q^2
To find the quantity that maximizes revenue, we take the derivative of R(q) with respect to q and set it equal to zero:
R'(q) = 29 - 0.02q = 0
0.02q = 29
q = 1450
Therefore, the quantity that maximizes revenue is 1450.
To find the price at this production level, we substitute q = 1450 into the demand equation:
p = 29 - 0.01(1450) = $14.50
So the price of each item at this production level is $14.50.
The total revenue at this price can be found by substituting q = 1450 and p = $14.50 into the revenue equation:
R(1450) = 1450(14.50) = $21,025
To learn more about the demand function visit : https://brainly.com/question/24384825
#SPJ11
10. A shopkeeper earns a profit of Rs 1 by selling one pen and earns a loss of 30
paise on sale of one pencil. In a particular month, he incurs a loss of Rs 5. In that
month, he sold 40 pens. How many pencils did he sell in that period?
He sold 116 pencils (approx) in that period.
To solve this problemAssume the store owner made x sales of pencils during that month.
A profit of one rupee every pen
One pencil costs 30 paise = Rs. 0.3, in loss.
40 pens sold for a total profit of 40 x Rs 1 = Rs 40
Pencil loss as a whole = x x Rs 0.3 = Rs 0.3x
Given, he loses Rs 5 during that month.
So, 40 - 0.3x = 5
0.3x = 35
x = 35/0.3
x = 116.67
Therefore, he sold 116 pencils approx in that period.
Learn more about profit here : brainly.com/question/23706629
#SPJ1
Which equation represents the graph?
y equals negative three halves times x plus 5
y equals negative two thirds times x plus 3
y equals two thirds times x minus 3
y equals three halves times x minus 5
An equation that represents the graph include the following: C. y equals two thirds times x minus 3.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.3 -1 0 -3
First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-3 + 1)/(0 - 3)
Slope (m) = -2/-3
Slope (m) = 2/3
At data point (0, -3) and a slope of 2/3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y + 3 = 2/3(x - 0)
y = 2x/3 - 3 i.e "y equals two thirds times x minus 3"
Read more on point-slope here: brainly.com/question/24907633
#SPJ1
help need this asap!
The requreid surface area of the sphere with a radius of 19 cm is 4536.46 cm².
To determine the exact surface area of the sphere with a diameter of 19 cm.
The surface area of the sphere is given as,
Surface area of the sphere = 4πr²
Substitute the value of the radius, r = 19 in the above formula,
Surface area of the sphere = 4*3.14*19²
= 4536.46 cm²
Thus, the requreid surface area of the sphere with a radius of 19 cm is 4536.46 cm².
Learn more about the sphere here:
https://brainly.com/question/12063484
#SPJ1
given the following: d: μ≥1000; e: μ<1000 d and e represent respectively.
Based on the information provided, d and e represent different statistical hypotheses about a population mean, denoted by. Specifically, the hypothesis d states that the population mean is greater than or equal to 1000, while the hypothesis e states that the population mean is less than 1000.
To put this into context, let's say that we are interested in studying the average income of workers in a certain city. We can collect a sample of data from a random sample of workers in the city, calculate the sample mean, denoted by x, and use it to make inferences about the population mean,. If we want to test the hypothesis that the average income is at least 1000 dollars, we can set up the null hypothesis as d: 1000 and the alternative hypothesis as not d: 1000. This means that we assume the population mean is 1000 or greater, and we want to see if there is enough evidence in the data to reject this hypothesis in favor of the alternative.
On the other hand, if we want to test the hypothesis that the average income is less than 1000 dollars, we can set up the null hypothesis as e: 1000 and the alternative hypothesis as not e: 1000. In this case, we assume the population mean is less than 1000, and we want to see if the data provide enough evidence to reject this hypothesis in favor of the alternative.
To know more about statistical hypotheses visit:-
https://brainly.com/question/31898256
#SPJ11
If a deli has 25 types of bread, 25 different kinds of meat, 15 kinds of cheese, and 55 types of condiments, how many sandwiches can you make
Deli can make 515,625 sandwiches.
Given that a deli has 25 types of bread, 25 different kinds of meat, 15 kinds of cheese, and 55 types of condiments, we need to find that how many sandwiches it can make,
So, the number of sandwiches it can make = 25 x 25 x 15 x 55
= 515,625
Hence the deli can make 515,625 sandwiches.
Learn more about fundamental counting principal click;
https://brainly.com/question/25193667
#SPJ1
please help me with bearings
The bearings of B from A in the given diagrams are shown to be :
a. 50 °b. 115 ° c. 223 °How to find the bearing of a location from another ?To be able to tell the bearing of B from A, you need to Identify and mark two points on a map or diagram of the area. Proceed to draw a straight line between these two points demarcating them clearly.
Employ a protractor in measuring the angle created between the aforementioned line and the north-south axis; this calculated measurement will be referred to as your "bearing."
Then, from the North - south line going up from A, you check the degree measure clockwise to B. Doing this, the bearings of B from A would be 50 °, 115° and 223 ° respectively.
Find out more on bearings at https://brainly.com/question/28782815
#SPJ1
If A is the set of all integers, choose the set B that will make the following statement false. B ⊆ A
B = {2.5, 3.5, 4.5} will make the statement false.
Option B is the correct answer.
We have,
A is the set of all integers.
And,
B ⊆ A
This means,
B is a subset of A where all elements in B is in A.
Now,
B = {1, 2, 3}.
This is true.
B = {2.5, 3.5, 4.5}
This is not true.
2.5, 3.5, and 4.5 are not integers.
They are real numbers.
B = {0}
This is true.
B = {-4, -1, 0, 5, 10}
This is true.
Thus,
B = {2.5, 3.5, 4.5} will make the statement false.
Learn more about numbers here:
https://brainly.com/question/17429689
#SPJ1
a right rectangular prism has a height of 17.5 cm. The area of the base of the prism is 18 square cm. what is the volume, in cubic cm, of the right rectangular prism?
The volume of the given rectangular prism is 315[tex]cm^3[/tex]
We have the information from the question:
A right rectangular prism has a height of 17.5 cm.
The area of the base of the prism is 18 square cm.
To find the volume, in cubic cm of the right rectangular prism.
We know that the volume of a right rectangular prism is given by-
Volume = A × h
Volume = (18)(17.5)
Volume = 315[tex]cm^3[/tex]
So the volume of the given rectangular prism is 315[tex]cm^3[/tex]
Learn more about Rectangular prism at:
https://brainly.com/question/1605212
#SPJ1
I need more help
(Worth 20 points)
Answer:
√(15^2 - 9^2) = √(225 - 81) = √144 = 12
√(15^2 + 9^2) = √(225 + 81) = √306
= 3√34
in a hypothesis test, if the computed p-value is less than 0.001, there is very strong evidence toa) fail to reject the null hypothesis.b) reject the null hypothesis.c) retest with a different sample.
A computed p-value less than 0.001 provides very strong evidence to reject the null hypothesis in a hypothesis test.
If the computed p-value is less than 0.001 in a hypothesis test, there is very strong evidence to reject the null hypothesis.
The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true. It represents the strength of evidence against the null hypothesis. A small p-value means that it is very unlikely to observe such an extreme test statistic under the null hypothesis, and therefore provides evidence against the null hypothesis.
The significance level, usually denoted by α, is the maximum allowable probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. The conventional significance level is 0.05, which means that we are willing to accept a 5% chance of making a Type I error.
If the computed p-value is less than the significance level, we reject the null hypothesis and conclude that the alternative hypothesis is supported by the data. A p-value less than 0.001 means that the observed result is highly unlikely to occur by chance alone, even at a very low significance level such as 0.1% or 0.01%. Therefore, we have strong evidence against the null hypothesis and can reject it in favor of the alternative hypothesis.
Learn more about null hypothesis at: brainly.com/question/28098932
#SPJ11
Show that the sequence {an} is a solution of the recurrence relation an = -3an-1 + 4an-2 if a.an = 0. b.an = 1. c.an = (-4)n. d.an = 2(-4)n + 3.
All four sequences (an = 0, an = 1, an = (-4)n, and an = 2(-4)n + 3) are solutions of the recurrence relation an = -3an-1 + 4an-2.
a. an = 0
This is a solution of the recurrence relation an = -3an-1 + 4an-2. To show this, we can start by substituting an = 0 and an-1 = 0 into the recurrence relation. We get:
0 = -3(0) + 4(0)
0 = 0
Since this is true, it follows that an = 0 is a solution of the recurrence relation.
b. an = 1
This is also a solution of the recurrence relation an = -3an-1 + 4an-2. To show this, we can start by substituting an = 1 and an-1 = 0 into the recurrence relation. We get:
1 = -3(0) + 4(1)
1 = 4
Since this is true, it follows that an = 1 is a solution of the recurrence relation.
c. an = (-4)n
This is also a solution of the recurrence relation an = -3an-1 + 4an-2. To show this, we can start by substituting an = (-4)n and an-1 = (-4)n-1 into the recurrence relation. We get:
(-4)n = -3((-4)n-1) + 4((-4)n-2)
(-4)n = -12((-4)n-1) + 16((-4)n-2)
(-4)n = 16((-4)n-2) - 12((-4)n-1)
Since this is true, it follows that an = (-4)n is a solution of the recurrence relation.
d. an = 2(-4)n + 3
This is also a solution of the recurrence relation an = -3an-1 + 4an-2. To show this, we can start by substituting an = 2(-4)n + 3 and an-1 = 2(-4)n-1 + 3 into the recurrence relation. We get:
2(-4)n + 3 = -3(2(-4)n-1 + 3) + 4(2(-4)n-2 + 3)
2(-4)n + 3 = -6(-4)n-1 - 9 + 8(-4)n-2 + 12
2(-4)n + 3 = 8(-4)n-2 - 6(-4)n-1 + 12
Since this is true, it follows that an = 2(-4)n + 3 is a solution of the recurrence relation.
To learn more about recurrence relation visit:
https://brainly.com/question/10636530
#SPJ4
Write and solve an equation to solve the following problem. be sure to define your variable and to state your answer in a complete sentence.jen, carrie, and fran are each thinking of a number. when you add their numbers together you get 207. jen’s number is 9 more than carrie’s, and fran’s number is 3 less than jen’s number. what is fran’s number?
Carrie's number is 64.
Jen's number is 64 + 9 = 73.
And Fran's number is 73 - 3 = 70.
Let's define our variables:
Let x be Carrie's number.
Then Jen's number is x + 9.
And Fran's number is (x + 9) - 3.
We know that when we add their numbers together, we get 207:
x + (x + 9) + ((x + 9) - 3) = 207
Simplifying the equation:
3x + 15 = 207
3x = 207 - 15
3x = 192
x = 192/3
x = 64
So Fran's number is 70.
Know more about variables here:
https://brainly.com/question/17344045
#SPJ11
PQRS is a kite. A and B are the midpoints of PQ and PS respectively. QD = DR and SC = CR. Prove that ABCD is a parallelogram.
The proof that ABCD is a parallelogram is given below.
In a parallelogram, the opposite sides of the quadrilateral are parallel to each other. Therefore, there are two sets of parallel sides.
The diagram for the given condition can be made as shown below in the attached image.
Now, consider the ΔPQS. Since A and B are the midpoints of the sides PQ and PS, respectively. Therefore, according to the basic proportionality theorem, AB║QS.
Similarly, consider the ΔQRS. Since QD = DR and SC = CR, therefore, D and C are the midpoints of the sides QR and SR, respectively. Therefore, according to the basic proportionality theorem, QS║DC.
As per the two conclusions drawn above, AB║QS and QS║DC. It can be concluded that AB║QS ║DC, therefore, AB║DC.
Further, in a similar manner consider ΔPQR and ΔPSR.
In ΔPQR, A and D are the midpoints of PQ and QR, respectively. Therefore, as per the Basic proportionality theorem the AD║PS.
In ΔPSR, B and C are the midpoints of PS and SR, respectively. Therefore, as per the Basic proportionality theorem the BC║PS.
As per the two conclusions drawn above, AD║PS and BC║PS. It can be concluded that AD║PS║BC, therefore, AD║BC.
Thus, ABCD is a parallelogram because of AB║DC and AD║BC.
Learn more about a parallelogram here:
https://brainly.com/question/29147156
#SPJ1
the password for a school's grading system is a 4-digit code. if the password is composed of digits one through nine, what is the probability that the password is composed of a one, a two, a three, and a four?
The total number of permutations of the four digits is 4 x 3 x 2 x 1 = 24.
To calculate the probability that the password for the school's grading system is composed of a one, a two, a three, and a four, we need to use the formula for permutations. A permutation is the number of ways that objects can be arranged in a specific order. In this case, we want to know the number of permutations of the four digits that make up the password.
There are nine possible digits to choose from, but we need to choose four specific digits: one, two, three, and four. The first digit can be any of the four digits we need, so there are four choices. The second digit can be any of the remaining three digits, so there are three choices. The third digit can be any of the remaining two digits, and the fourth digit must be the remaining digit.
Therefore, the total number of permutations of the four digits is 4 x 3 x 2 x 1 = 24. However, this is only the numerator of the probability fraction. The denominator is the total number of possible 4-digit passwords, which is 9 x 8 x 7 x 6 = 4,536.
So the probability that the password for the school's grading system is composed of a one, a two, a three, and a four is 24/4,536, which simplifies to 1/189. This means that there is a very small chance of the password being composed of these specific digits.
Learn more about probability brainly.com/question/30034780
#SPJ11
