a) Z-score for Patrisse test grade is 0.7288
b) z-score for Makayla test grade is -0.7441
c) Patrisse did better.
What is z- score?
A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
Z-score for Patrisse test grade.
X= 81.4, [tex]\mu[/tex] = 72.8, [tex]\sigma[/tex] = 11.8
Z= x- [tex]\mu[/tex] / [tex]\sigma[/tex]
Z= 81.4 - 72.8/ 11.8
Z= 0.7288
Now, z-score for Makayla test grade.
X= 60.6, [tex]\mu[/tex] = 67, [tex]\sigma[/tex] = 8.6
Z= x- [tex]\mu[/tex] / [tex]\sigma[/tex]
Z= 60.6 - 67/ 8.6
Z= -0.7441
Hence, Patrisse did better as she had better z- score.
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Pepperidge Farm Goldfish is a snack food for which 40% of it's calories come from fat. Rold Gold Pretzels receive 9% of their calories from fat. How many grams of each would be needed to make 620 g of a snack mix for which 15% of the calories are from fat?
1) Simplify the following expressions: a) sin²108° + sin² 18°
Note that
108° = 90° + 18°
so
sin(108°) = sin(90° + 18°) = sin(90°) cos(18°) + cos(90°) sin(18°) = cos(18°)
Then
sin²(108°) + sin²(18°) = cos²(18°) + sin²(18°) = 1
by the Pythagorean identity.
The value of the expression sin²(108°) + sin² (18°) will be 0.9986.
What is a expression? What is a mathematical equation? What is Equation Modelling? What are trigonometric functions?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. The six - trigonometric functions are -
sinecosinetangentcosecseccotangentWe have the following trigonometric equation -
sin²(108°) + sin² (18°)
We have the following expression -
sin²(108°) + sin² (18°)
(0.95)² + (0.31)²
0.9025 + 0.0961
0.9986
Therefore, the value of the expression sin²(108°) + sin² (18°) will be 0.9986.
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Instructions: Match each equations with correct type of event.
P(A) · P(BA)
P(A) + P(B)
PA and B)
P(A)
P(A) · P(B)
P(A) + P(B) - P(A and B)
The question is incomplete. Below you will find the missing contents.
The correct match of events with order are,
P(A)P(B|A) - Dependent event P(A)+P(B) - Mutually exclusive events P(A and B)/P(A) - Conditional events P(A) . P(B) - Independent Events P(A)+P(B) -P(A and B) - not Mutually exclusive events.When two events A and B are independent then,
P(A and B)=P(A).P(B)
when A and B are dependent events then,
P(A and B) = P(A) . P(B|A)
When two events A and B are mutually exclusive events then,
P(A and B)=0
So, P(A or B) = P(A) + P(B) - P(A and B) = P(A) + P(B)
P(A) + P(B) = P(A or B)
When events are not mutually exclusive then the general relation is,
P(A or B) = P(A) + P(B) - P(A and B)
If the probability of the event B conditioned by A is given by,
[tex]\mathrm{P(B|A)=\frac{P(A~and~B)}{P(A)}}[/tex]
Hence the correct match are -
[tex]\mathrm{P(A)P(B|A)\rightarrow}[/tex] Dependent event [tex]\mathrm{P(A)+P(B)}\rightarrow[/tex] Mutually exclusive events [tex]\mathrm{\frac{P(A ~and ~B)}{P(A)}\rightarrow}[/tex] Conditional events [tex]\mathrm{P(A) . P(B)\rightarrow}[/tex] Independent Events [tex]\mathrm{P(A)+P(B) -P(A ~and ~B)\rightarrow}[/tex] not Mutually exclusive events.Learn more about Probability of Events here -
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what is the mid point of 3,2 and -3,4?
Answer
(0,3)
Step-by-step explanation:
from mid point (x+x)/2, (y+y)/2((3+-3)/2,(2+4)/2)(0/2, 6/2)(0, 3)Urgent!!!
Use the Law of Sines to find all missing sides and angles of the following triangle (side b, side
c, and angle C). Approximate your answers to the nearest tenths. a = 35.0 km, A = 13.0°, B =
65.3°
Answer:
A = 13 degrees
B = 65.3 degrees
C = 180 - (13 + 65.3) = 101.7 degrees
Side a = 35 km
Side b = 141.4 km
Side c = 152.4 km
What is the rule for the reflection?
rx-axis (x, y) - (-x, y)
ry-axis (x, y) (-x, y)
rx-axis (x, y) - (x, y)
ry-axis (x, y) (x, −y)
When reflected over ry-axis (x, y) (-x, y) , rx-axis (x, y) (x,-y) , Option A and D is the correct answer.
What is rule for the reflection ?The rule for reflection is when an object or a coordinate point is reflected over x axis then the coordinate of the x axis remains the same while the y coordinate changes to be additive inverse.
Vice Versa happens when reflected over y axis.
So,
rx-axis (x, y) - (-x, y) --> (x,-y)
ry-axis (x, y) (-x, y)
Therefore Option A and D is the correct answer.
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Answer: its A not A & D
Step-by-step explanation:
Please help and fast for brainliest
The graph shows the number of gallons of white paint that were mixed with gallons of green paint in various different ratios:
Draw the graph on a grid. The title is Mixing Paint. The horizontal axis label is Green Paint in gallons. The scale is 0 to 24 in increments of 3. The vertical axis label is White Paint in gallons. The scale is 0 to 72 in increments of 9. Plot points at the ordered pairs 3,9 and 6,18 and 9,27.
The number of gallons of white paint mixed with 1 gallon of green paint is ______.
Answer:
3 gallons
Step-by-step explanation:
For every value of green ( 'x') ....white is 3 times as much
for 1 gallon green ====> 3 gallons white
What is the approximate area of the shaded sector in the circle shown below
A.29.04 in^2
B.13.51 in^2
C.7.26 in^2
D.6.75^2
Answer:
please provide the diagram
Step-by-step explanation:
for the solution figure is necessary so provides us to solve this problem
2. Mike is looking to purchase a Ford Explorer, which has a sticker price of $32,415. He's able to negotiate $3,000
off sticker price, and the tax rate is 6.5%. License and title fees are $395. If he trades in his minivan for $9,000
(deducted from the negotiated price before taxes), the monthly payment will be $500.95 for 60 months. He is
also offered a lease with $2,900 down and payments of $429 for 36 months.
a) How much will Mike pay total if he chooses the lease option?
b) How much more will he pay in the first three years if he chooses to buy instead?
c) How much interest will he pay if he buys?
d) Which option would you choose? Explain.
3. Maya bought a new Ford Focus for $17,400. She made a down payment of $4,000 and made monthly payments
of $396 for three years. Find the APR.
Answer:
.wfhytrsssssssssd
Step-by-step explanation:
dddddddddddddddddd
Complete the point-slope equation of the line through (-4, 8) and (4, 4).
Use exact numbers.
y-4=
Answer:
y-4=-1/2(x-4)
Step-by-step explanation:
point slope form: y-y1=m(x-x1)
every time x increases by 8, y decreases by 4. slope can be found by rise/run. the slope is -4/8 which is -1/2, which means m=-1/2. in the given equation, it said y-4. It plugged in 4 for y1, meaning it was talking about the second given point, which was (4,4). plug in 4 for x and you get y-4=-1/2(x-4)
Tìm số dư trong phép chia 3^{2020} chia cho 13
Your question translates to computing [tex]3^{2020} \pmod {13}[/tex].
Recall Euler's theorem: if [tex]\gcd(a,n)=1[/tex] (that is, [tex]a[/tex] and [tex]n[/tex] are relatively prime), then [tex]a^{\varphi(n)}\equiv1\pmod n[/tex], where [tex]\varphi(n)[/tex] denotes Euler's totient function, which counts the number of positive integers relatively prime to [tex]n[/tex].
Since 13 is prime, we have [tex]\phi(13)=12[/tex]. Then by Euler's theorem,
[tex]3^{12} \equiv 1 \pmod{13}[/tex]
Now, observe that 2020 = 168×12 + 4, so that
[tex]3^{2020} \equiv 3^{168\times12+4} \equiv \left(3^{12}\right)^{168} \times 3^4 \equiv 1^{168} \times 3^4 \equiv 3^4 \pmod{13}[/tex]
and since 3⁴ = 81 = 6×13 + 3, we end up with
[tex]3^{2020} \equiv 81 \equiv 3 \pmod{13}[/tex]
so the remainder upon dividing 3²⁰²⁰ by 13 is 3.
Expand:
4(5x+5) - 3(2x + 4)
Answer:
14x + 8
Explanation:
⇒ 4(5x+5) - 3(2x + 4)
distribute inside parenthesis
⇒ 4(5x) + 4(5) - 3(2x) - 3(4)
multiply the variables
⇒ 20x + 20 - 6x - 12
collect like terms
⇒ 20x - 6x + 20 - 12
subtract like term
⇒ 14x + 8
4 x 5x = 20x
4 x 5. = 20
-3 x 2x = - 6x
-3 x 4 = - 12
Line them up, collect like terms & simplify
20x + 20 - 6x - 12
20x - 6x = 14x
20 - 12 = 8
Thus, answer is 14x + 8
Hope this helps!
20
Find the standard deviation of
the given data rounded to the
nearest hundredth.
12, 53, 141, 219, 500
Σ (x-mean)2
n
0 =
σ= [?]
The standard deviation of the data to the nearest hundredth is 173.01.
What is standard deviation?Standard deviation is used to determine how the values in a group differs from the mean of the values in the group. It is a measure of variation.
In order to determine the standard deviation, take the following steps:
Determine the mean of the observation: 185
Determine the difference between each value and the mean and then square the result:
Determine the mean of the sum of the squared differences and then find the square root of the mean:
Following these steps, the standard deviation is 173.01
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x² +5-x when x = 5
Jamaymaykgajwnammagmaganhsnagm
Answer:
25
Step-by-step explanation:
you first solve for the expontes. 5 to the power of 2 is 25 plus 5 is 30. subtract 5 from that and we're back at 25
Answer:
25
Step-by-step explanation:
When we plug in 5 for x, we get 25+5-5=25.
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.8 years, and standard deviation of 0.7 years.
If you randomly purchase one item, what is the probability it will last longer than 6 years?
Round answer to three decimal places
The probability of 6 years or more, so we want the complement,
1 - 0.98533 = 0.01467 1.467% chance, not very likely.
What is Z-score?A z score is a type of statistical measurement that gives an idea of how far a raw score is from the mean of a distribution. A z score is used in a z test for hypothesis testing.
Here, Because you are looking for the mean of a group of 7.8, the standard deviation will shrink by a factor of √6
Old standard deviation = 0.7,
new standard deviation = 0.7/√6 = 0.64254
You need to find a z-score and then convert your z-score to a probability.
z-score = (your score - average)/ std dev
z-score = (7.8 - 6)/0.64254
z-score = 2.1789
To convert a z-score either look it up on a table or use a calculator.
But z-tables are designed to shade to the left, which means this is the probability that the mean life is 6 years or less. We want the probability of 6 years or more, so we want the complement, 1 - 0.98533 = 0.01467
1.467% chance, not very likely.
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*Need Help*Match each rational expression to its simplest form.
Identify how the two trianiges are congruent. Fill in the blank below the triangles with SSS, SAS, ASA, AAS, or HL. If the two triangles are not
congruent, type not congruent.
A4X4
Blank 1:
Blank 2:
Blank 3:
Blank 4:
Question 2 (1 point)
Answer:
Blank 1 = SAS
Blank 2 = HL
Black 3 = ASA
Blank 4 = SSS
SAS - when two corresponding sides and one corresponding angles are equal HL - in a right angle triangle when corresponding hypotenuse and length are equal ASA - when 2 corresponding angles and one corresponding side are equal when all the sides of triangle is equal to other.the exppreson of 10x^2-7
The complete question is :
Question: What is the coefficient in the expression 10x²-7?
The coefficient in the expression [tex]10x^{2} -7[/tex] is 10
What is Coefficient?A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
According to the question,
The expression given is [tex]10x^{2} -7[/tex]
The variable given is x
We need to find the coefficient in the expression.
In the given expression x is the variable and the number before the x is coefficient which is 10 .
Hence the coefficient in the expression is 10.
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Support her statements using scale factors of 5 and 6.
Reflection: Marissa wants to describe the relationship between the scale factor and perimeter of an image and its pre-image and between the scale factor and area of an image and its pre-image. What should she say about the relationship between the scale factor and perimeter of an image and its pre-image? What should she say about the relationship between the scale factor and area of an image and its pre-image? Support her statements using scale factors of 5 and 6.
Answer:
The relationship between the scale factor and perimeter of an image and its pre-image is a, b = perimeter = 2a + 2b. the relationship between the scale factor and area of an image and its pre-image is k∧2 (ab).
Step-by-step explanation:
Relationship between the scale factor and perimeter of an image and its pre-image.
Scale factor = k
Pre-image lengths: a, b = perimeter = 2a + 2b
Image lengths: ka, kb = perimeter = 2ka + 2 kb = k (2a + 2b) = 2 * preimage perimeter.
She has to say that the perimeter of the image is the perimeter of the preimage times the same scale factor.
What should she say about the relationship between the scale factor and area of an image and its pre-image?
area of the pre-image = ab
are of the image = (ka)(kb) = k^2 (ab)
The area of the image is the area of the preimage times the square of the scale factor.
Support her statements using scale factors of 5 and 6.
Scale factor 5
length of the pre-image = 3 x 4 = perimeter = 2 (3 + 4) = 2(7) = 14
length of the image = 3*5 x 4*5 = 15 x 20 = perimeter = 2 (15 + 20) = 2 (35) = 70
14 * 5 = 70 which shows the prediction
area of the pre-image = 3 * 4 = 12
area of the image = 15 * 20 = 300
12 * (5^2) = 12*25 = 300 which is the value predicted.
Now you can do the same using scale factor 6.
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Algebra 2 urgent I need help quickkk 20 points !!!
Answer:
(-3, -13)
(-1, -7)
(1, -1)
(3, 5)
(5, 11)
Step-by-step explanation:
Plug x into the equation y = 3x - 4 for each value of x to obtain the y value.
For example:
y = 3(3) - 4
y = 9 - 4
y = 5
five percent of a batch of fuel was found faullty if 27 fuses were faulty how many were inspected the price of internet service is decreased by 7% to 52.00 what is the original price
There are 540 fuses in total and the original price of the internet is $55.91
How to work with percentages?
a) We know that 5% of the fuses are faulty, and there are 27 faulty fusses, then we can write:
5% = 27
100% = x
We want to find x, to do that, we can write:
x = 27*(100%/5%) = 27*20 = 540
There are 540 fuses in total.
b) Now we know that the original price is P, and when we decrease it by 7%, then new price is $52.00
Then we can write:
$52.00 = P*(1 - 7%/100%)
$52.00 = P*(0.93)
$52.00/0.93 = P = $55.91
The original price is $55.91
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《QUESTION 1》
The length of the side of a square is 50 cm and the breadth of a rectangle is 25 cm. If the areas of the square and the rectangle are equal, find the length of the rectangle.
《QUESTION 2》
A wire is in the shape of a rectangle with length 6 cm. It is bent to form a square whose side is 5 cm. Find the breadth of the rectangle. Also, calculate the areas of both the rectangle and the square and find which shape encloses more areas.
The length of the rectangle is 100cm.
The breadth of the rectangle is 4cm.
The square encloses more area than the rectangle.
What is the length of the rectangle?The first step is to determine the area of the square.
Area of a square = length² = 50² = 2500 cm²
Area of a rectangle = length x width
length = area / width
2500 / 25 = 100cm
What is the breadth of the rectangle?
The first step is to determine the perimeter of the square.
Perimeter = 4 x length
4 x 5 = 20cm
Perimeter of a rectangle = 2(length + width)
breadth = (perimeter / 2) - length
(20 / 2) - 6
10 - 6 = 4cm
Area of the square = 5 x 5 = 25
Area of the rectangle = 6 x 4 = 24
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Please help!!! I will give 20 points to the correct answer !! Thanks so much
The graphs below have the same shapes. What is the equation for the red graph?
The equation for the red graph will be g(x) = x² + 3.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The function f(x) is given below.
f(x) = x²
Then the function g(x) will be given as
g(x) = x² + 3
Then the equation for the red graph will be g(x) = x² + 3.
The missing graph is given below.
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You observe a plane approaching overhead and assume that its speed is 700 miles per hour. The angle of elevation of the plane is 15° at one time and 59° one minute later. Approximate the altitude of the plane. (Round your answer to two decimal places.)
Answer:
3 miles
2.73 miles=3 miles
Find the x-intercept of the line whose equation is 8x + 2y = 4.
Answer: Hope this helps you
1/2
Step-by-step explanation:
To find the x-int of any equation, you will need to replace the y with a 0 since when the x-int is when y is 0.
8x+2y = 4 ➨ 8x+2*0 = 4
Now I will do 2*0 which anything times 0 is equal to 0. And we are left with the equation of:
8x = 4
Now I will divide both sides by 8, which isolates our x.
x = 1/2
The x-int is 1/2.
If 13 metres of a uniform iron rod weights 23.4 kg then what will be the weight of 6 metres of the same rod?
Answer:
Solution:
Here,
[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline 13 \rm{m}& \rm{23.4kg} \\ \hline \rm{6m}&?\\ \hline\end{array}[/tex]
Weight of 13 m of rod=23.4 kg
Weight of 1 m of rod=23.4/13 kg
[less length,less weight]
Weight of 6 m of rod=23.4/13 ×6 kg=10.8 kg
[more length,more weight]
Thus,the weight of 6 m of rod is 10.8 kg.
Alternative method:
Let,the required weight be x kg.
Then,
[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline \rm{13m}& \rm{23.4 \: kg }\\ \hline \rm{6m}& \rm{x =? } \\ \hline\end{array}[/tex]
We know that,
More length of iron rod([tex]\red{\uparrow}[/tex]) will have the more weight([tex]\red{\uparrow}[/tex]).
So,using the rule of direct proportion;
i.e. Ratio of length=Ratio of weight
[tex] \displaystyle{ \frac{13}{6} = \rm\frac{23.4}{x} }[/tex]
[tex] \rm{13x = 6 \times 23.4}[/tex]
[tex] \rm{x = \displaystyle{ \frac{6 \times 23.4}{13} }}[/tex]
[tex] \therefore{x = 10.8}[/tex]
Thus,the weight of 6 m long iron rod is 10.8 kg.
An avid traveler is investigating whether travel websites differ in their pricing. She chooses a random sample of 32 hotel rooms from across the state and notes the price of each room from site A and site B. The mean difference (site A – site B) in the prices for the rooms is $5.49 with a standard deviation of $18.65.
Assuming the conditions for inference have been met, is there evidence that the prices of hotel rooms from site A and site B are different, on average? Use a significance level of a = 0.05.
A. Because the P-value is less than α, there is evidence that the prices of hotel rooms from site A and site B are different, on average.
B. Because the P-value is greater than α, there is evidence that the prices of hotel rooms from site A and site B are different, on average.
C. Because the P-value is less than α, there is not sufficient evidence that the prices of hotel rooms from site A and site B are different, on average.
D. Because the P-value is greater than α, there is not sufficient evidence that the prices of hotel rooms from site A and site B are different, on average.
Bob has saved $535 each month for the last 3 years to make a down payment on a house. The account earned an interest rate of .34 percent per month. How much money is in Bob's account?
Answer:
The account has $18,795.02.
Step-by-step explanation:
The account has $18,795.02.
3 years * $535 = $1,605
$1,605 * .0034 = $5.481
$5.481 * 36 (months) = $197.146
$18,795.02 = $1,605 + $197.146
Can you conclude that this parallelogram is a rectangle ? Explain. No;the diagonals do not bisect two angles of the parallelogram. No;the diagonals may not be congruent. Yes; the diagonals are perpendicular
The answer to the question on Parallelograms being rectangles is that; No; the diagonals may not be congruent
How to Identify the properties of a Parallelogram?1) We cannot conclude that the parallelogram is a rectangle but we can say that all rectangles are parallelograms.
2) The explanation for number 1 above is that the parallelogram's diagonals may not be equal or congruent but in rectangles diagonals are always equal and bisect each other.
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