The required probability that X is less than 16 is approximately 0.15866 or 15.86%.
What is the Z -a score?A Z-score is stated as the fractional model of data point to the mean using standard deviations.
Here,
We can use the standard normal distribution to find the probability that a normally distributed random variable, X, is less than a certain value. To use the standard normal distribution, we need to standardize X by subtracting the mean and dividing by the standard deviation:
Z = (X - μ) / σ
In this case, X has a mean of 25 and a standard deviation of 9,
Z = (16 - 25) / 9
z = -1
To find the probability that X is less than 16, we need to find the corresponding value of Z using the standard normal distribution table or a calculator.
P(Z < -1) ≈ 0.15866
Therefore, the probability that X is less than 16 is approximately 0.15866 or 15.86%.
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Discount % is always calculated on the:
a) CP ( cost price).
b) SP ( selling price).
c) MP ( marked price).
d) None of these.
What is the solution set to the inequality w+ 4<4 (w - 2)?
Select a ray. Move the point on the ray to the correct place on the number line.
-7 -6 -5 -4
H
->
(-)
-3 -2 -1
0 1 2
--
31
3
4 5 6 7
--
+
The solution set to the inequality is w > 3
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
w+ 4<4 (w - 2)
Open the bracket
So, we have the following representation
w+ 4 < 4w - 8
Evaluate the like terms
So, we have the following representation
12 < 3w
Divide by 3
4 < w
So, we have
w > 4
See attachment for number line
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Suppose that the amount of algae in a pond doubles every 5 hours. If the pond initially contains
10 pounds of algae, how much algae will be in the pond after 20 hours?
Answer:
160 pounds of algae
Step-by-step explanation:
10 times 2 is 20 ( first 5 hours )
20 times 2 is 40 (10 hours)
40 times 2 is 80 (15 hours)
80 times 2 is 160 ( 20 hours)
there would be 160 pounds of algae
Find the value of x. Round to the
nearest tenth.
X
12
x= [?]
Enter
Answer: 2x + 12
Step-by-step explanation:
Зу = 4х+5
4y = 4х +7
Answer:
y = 2; x = 1/4
Step-by-step explanation:
We can solve for y then x using elimination. We can multiply the first equation by -4 to cancel out the xs:
[tex]-1(3y=4x+5)\\\\4y=4x+7\\-3y=-4x-5\\\\y=2\\\\[/tex]
Now, we can plug in this 2 for y in any of two equations to find x:
[tex]3(2)=4x+5\\6=4x+5\\1=4x\\1/4=x[/tex]
if y x 3 equals to 3/5 y
Answer:
since y = 0 when x = 0
Step-by-step explanation:
We can start by solving for y in the equation:
y * x = 3/5 y
Dividing both sides by y:
x = 3/5
So the equation y * x = 3/5 y can be simplified to:
y = 5/3 x
This equation shows that there is a proportional relationship between y and x, where y is always equal to 5/3 times x. This relationship can be represented on a graph by plotting points (x, y) and drawing a line through them. The slope of the line will be 5/3, and the y-intercept will be 0, since y = 0 when x = 0.
Answer:
y = ±1/√5
Step-by-step explanation:
3y = 3/5y
⇒3y×5y = 3
⇒15y² = 3
⇒y² = 3/15
⇒y² = 1/5
⇒y = ±1/√5
Find the output, y, when the input, a, is 7
Answer: Y would be 4
If you look at the graph and find 7 on the x axis where the inputs are, you can see that if you go up, the only output for 7 is 4.
The annual profits for a company are given
in the following table, where x represents
the number of years since 2006, and y
represents the profit in thousands of
dollars. Write the linear regression
equation that represents this set of data,
rounding all coefficients to the nearest
hundredth. Using this equation, estimate
the calendar year in which the profits
would reach 482 thousand dollars.
Years since 2006 (x)
0
1
2
3
4
5
Profits (y)
(in thousands of dollars)
147
167
209
239
250
267
The linear regression of the data is given as follows:
y = 25.1x + 150.4.
The estimate for the year in which the profit would reach $482,000 is of:
2019.
How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
The points for this problem are given as follows:
(0, 147), (1, 167), (2, 209), (3, 239), (4, 250), (5, 267).
Hence the equation is of:
y = 25.1x + 150.4.
The estimate for the year in which the profit would reach $482,000 is x years after 2006, when y = 482, hence:
482 = 25.1x + 150.4.
x = (482 - 150.4)/25.1
x = 13.
2006 + 13 = 2019 -> year.
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given the set [1,2,3,5,8,13,21,34,55}, how many integers between 3 and 89 cannot be written as the sum of excatly two elements of the set?
The final count of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set is 39.
To determine the number of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set {1, 2, 3, 5, 8, 13, 21, 34, 55}, we can use a process of elimination.
First, we can list all the possible sums of two distinct elements of the set. This gives us a total of 28 sums.
Next, we can identify all the integers between 3 and 89 that can be expressed as the sum of two distinct elements of the set. We can do this by checking each integer between 3 and 89 to see if it can be written as a sum of two elements of the set. If an integer can be written as a sum of two elements of the set, we can cross it off the list.
After eliminating all the integers that can be written as a sum of two elements of the set, we are left with the integers that cannot be expressed as such.
In summary, we can determine the number of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set by listing all possible sums, identifying the integers that can be expressed as such sums, and eliminating them from the list.
The remaining integers are those that cannot be expressed as the sum of exactly two elements of the set.
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Use proportions to determine 23% of what number is 81.3. Round to the nearest hundredth.
Consider the original coordinates of the vertices of a parallelogram.
A (-2, 4)
B (4,4)
C (2,-2)
D(-4,-2)
According to the information, the area of the parallelogram plotted from the points would be: 36 cm²
How to find the area of the parallelogram?To find the area of the parallelogram we must divide the parallelogram into a quadrilateral section and another triangular section and find the area of these segments.
According to the above, we can infer that the area of the quadrilateral zone would be
a = b*ha = 4*6a = 24On the other hand, the area of the triangular section would be:
a = b*h/2a = 2 * 6 / 2a = 12 / 2a = 6Additionally, we must multiply the area of the triangular segment by two because there are two triangular sections in the parallelogram. Finally we have to add the area of the quadrilateral and triangle segments to get the total area.
6 * 2 = 1212 + 24 = 36Note: This question is incomplete. Here is the complete information:
TASK
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Which ordered pairs are in the solution set of the system of linear inequalities?
y2-3x+2
y< 2x+3
Answer: 2
Step-by-step explanation:
Suppose your home is located at (0, 0) on a coordinate plane. The school is located 5 miles west of your home. The playground is 3 miles south of the school. What is the shortest distance, in miles, between your home and the playground? Round your answer to the nearest tenth
The shortest distance is 5.83 miles as we calculate this by distance formula.
A distance formula is a formula used to find the distance between any two points only if the coordinates are known. These coordinates can be on the x-axis, y-axis, or both. Suppose we have two points, P and Q, in the XY plane. Point P has coordinates (x1,y1) and Q has coordinates (x2,y2). Then the formula for the distance PQ between two points is:
PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])
The school is located 5 miles west of your home the co ordinate is (-5,0)
The playground is 3 miles south of the school so co - ordinate is (0,-3)
shortest distance = PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])
√([tex]5^{2} +3^{2}[/tex]) = √34
=5.830 miles
And this Question also can be do by right angle triangle method
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3. a computer password consists of two lowercase letters followed by a capital letter and four digits. find the total number of possible passwords.
The total number of possible passwords is 17,576,000.
There are several steps involved in calculating the total number of possible passwords.
Step 1: Determine the number of possible choices for the first lowercase letter. Since there are 26 letters in the alphabet, and the password consists of lowercase letters, there are 26 choices for the first letter.
Step 2: Determine the number of possible choices for the second lowercase letter. Since there are 26 letters in the alphabet and repetition is allowed, there are 26 choices for the second letter.
Step 3: Determine the number of possible choices for the capital letter. Since the password requires a capital letter, there are 26 choices for this position.
Step 4: Determine the number of possible choices for the first digit. Since there are 10 digits (0-9), there are 10 choices for the first digit.
Step 5: Determine the number of possible choices for the second digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the second digit.
Step 6: Determine the number of possible choices for the third digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the third digit.
Step 7: Determine the number of possible choices for the fourth digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the fourth digit.
Step 8: Multiply the number of choices for each position together to get the total number of possible passwords.
Using the multiplication rule of counting, we get:
Total number of possible passwords = (Number of choices for the first lowercase letter) x (Number of choices for the second lowercase letter) x (Number of choices for the capital letter) x (Number of choices for the first digit) x (Number of choices for the second digit) x (Number of choices for the third digit) x (Number of choices for the fourth digit)
Total number of possible passwords = 26 x 26 x 26 x 10 x 10 x 10 x 10
Total number of possible passwords = 17,576,000
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A 13-ft by 27-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 384 ft^2, how wide is the walkway?
Answer:
w = 25 / 4 feet wide.
Step-by-step explanation:
Let's call the width of the walkway "w."
The area of the rectangular pool is 13 * 27 = 351 ft^2.
The area of the walkway can be calculated by adding up the area of four rectangles, one around each side of the pool:
2 * (13 + w) * w + 2 * (27 + w) * w = 384
Expanding the equation:
2 * 13w + 2w^2 + 2 * 27w + 2w^2 = 384
Combining like terms:
2w^2 + 40w = 384
Solving for w^2:
2w^2 + 40w - 384 = 0
Using the quadratic formula:
w = (-40 ± √(40^2 - 4 * 2 * -384)) / (2 * 2)
Simplifying:
w = (-40 ± √(1600 + 3072)) / 4
w = (-40 ± √4272) / 4
w = (-40 ± 65) / 4
w = (25 / 4) or (-105 / 4)
Since w must be a positive value, w = 25 / 4 feet wide.
Answer:look it up frfr
Step-by-step explanation:
Luis wants to buy a skateboard that usually sells for $79.86. All merchandise is discounted by 12%. What is the total cost of the skateboard if Luis has to pay a state sales tax of 8.25%. Round your intermediate calculations and answer to the nearest cent.
The total cost of the skateboard is $
The total cost of the skateboard is $76.07.
What is the total cost of the skateboard?The first step is to determine the price of the skateboard after the 12% discount. A discount reduces the price of an item.
Price after discount = price before discount x (1 - percent discount)
$79.86 x (1 - 12/100)
$79.86 x (1 - 0.12)
$79.86 x 0.88
= $70.28
Price after the sales tax = (1 + sales tax) x price after discount
= (1 + 8.25/100) x $70.28
(1 + 0.0825) x $70.28
1.0825 x $70.28 = $76.07
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ABCD is a rectangle with sides 8cm and 6cm PQRS is a rhombus
obtained by joining the midpoints of the sides of the rectangle. find
a)The lengths of the diagonals of PQRS?
b)The area of PQRS?
The lengths of the diagonals of PQRS will be 8 cm and 6 cm. Then the area of the rhombus PQRS will be 24 square cm.
What is the area?Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.
The diagonals of the rhombus will be the same as the dimension of the rectangle that is 8 cm and 6 cm.
Then the area of the rhombus is given as,
A = (Product of diagonal of rhombus) / 2
A = (8 x 6) / 2
A = 48 / 2
A = 24 square centimeters
The lengths of the diagonals of PQRS will be 8 cm and 6 cm. Then the area of the rhombus PQRS will be 24 square cm.
The diagram is shown below.
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Two joggers run 8 miles and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile they must travel to return to their starting position?
Answer:
A. 9.4 mi
Step-by-step explanation:
Sketch a right triangle with legs of 8 and 5. Shortest distance back to the starting point is the hypotenuse (h) of the triangle:
h² = 8² + 5² = 89
h = √89 = 9.43 mi
I need help fast with this question
The value of the given function for x=122 is 5 and x=-346 is -7.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is f(x)= ∛(x+3).
To find f(122):
Substitute x=122 in the given function, we get
f(122)=∛(122+3)
= ∛125
= ∛5³
= 5
To find f(-346):
Substitute x=-346 in the given function, we get
f(122)=∛(-346+3)
= ∛-343
= ∛(-7)³
= -7
Therefore, the value of the function for x=122 is 5.
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I need to find the value of x and it's a horizontal line or whatever the cross over like a x (3x-3)°147°
What is the positive solution to the equation 0= 1/4x^2-4
answers;
4
1
-1
-4
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{4} {x}^{2} - 4 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{4} {x}^{2} = 4[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} = 4 \times 4[/tex]
[tex]\qquad \sf \dashrightarrow \: x = \sqrt{4 \times 4} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = \pm4[/tex]
[ but since we have been asked for positive solution, it will be 4 ]
Hence, the correct choice is : A.) 4
A rectangle is 13 feet long and has a diagonal that is 20 feet long. What is the length of the width?
which function represents an exponential decay function with a y-intercept of -3?
a. f(x) = (0.5)^x - 4
b. f(x) = (0.5)^x - 3
c. f(x) = 2^x - 4
d. f(x) = 2^x - 3
Answer:
A
Step-by-step explanation:
The line has a negative slope, with a y-intercept of (0,-3), and an x-intercept of (-2,0)
Solve for x *
est
45
O x = 50
O x = 8
O x = 48.2
O x = 40.5
20
S
18
R
The value of x is given as follows:
x = 40.5.
What are similar triangles?Similar triangles share these two features:
Congruent angles, that is, angles that have the same measure.Proportional side lengths.The two triangles in this problem are similar, with the bisection, hence the proportional relationship for the side lengths is given as follows:
x/45 = 18/20
The relationship can be simplified as follows:
x/45 = 0.9.
Applying cross multiplication, the value of x is obtained as follows:
x = 45 x 0.9
x = 40.5.
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2. Mel uses one fourth of a yard of ribbon to make a hair bow. How many hair bows can Mel make with 1 yard of ribbon? show your work and explantion.
Answer:
Step-by-step explanation:
1/4 is one bow.
1/4 *4 is 1 yard.
mel can make 4 bows.
If 4 is added to twice the number n, the result is the same as if n were increased by 7. What is the value of n?
Answer:
n = 3
Step-by-step explanation:
Starting equation:
2n + 4 = n + 7
Subtract by n on both sides:
n + 4 = 7
Subtract 4 on both sides
n = 3
Check to see if the answer works:
2(3) + 4 = 3 + 7
6 + 4 = 3 + 7
10 = 10
The solution works
n = 3
rectangle abcd is dilated by a scale factor of 1/4 to form a’b’c’d’. point t is the center of dilation and lies on segment ab as shown
The slope of A'B' is 0 and the length of A'B' is 1/4(5) = 1.25 units.
What is transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
The line AB has the following coordinates.
A = (1, 4)
B = (6, 4)
The distance between AB is given as:
AB = √(6 - 1)² + (4 - 4)²
AB = √(5)²
AB = 5
The slope of AB = 0.
For the dilated rectangle the slope remains the same.
The slope of A'B' is 0 and the length of A'B' is 1/4(5) = 5/4 = 1.25 units.
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The correct question is:
Resuelve los siguientes ejercicios sobre raíces cuadradas.
15. Observa la siguiente suma de radicales. Luego, de-
termina sí las proposiciones son verdaderas (V) o
falsas (F).
-10√3+√12+8√3
Turea
Solo es posible sumar el primer y el tercer
sumando, ya que son los únicos semejantes.
al
La suma de los tres radicales es igual a cero.
La suma de los tres radicales es
1-2√3+√2.
La diferencia entre el tercer y el primer l
sumando es igual a 18√3.
Answer:
La proposición "La suma de los tres radicales es igual a cero" es falsa. Si sumamos los tres radicales, tenemos:
-10√3 + √12 + 8√3 = (-10 + 8)√3 + √12 = -2√3 + √12.
La proposición "La suma de los tres radicales es 1-2√3 + √2" es falsa, ya que la suma real de los tres radicales es -2√3 + √12.
La proposición "La diferencia entre el tercer y el primer sumando es igual a 18√3" es falsa, ya que la diferencia real entre el tercer y el primer sumando es 8√3 - (-10√3) = 8√3 + 10√3 = 18√3.
Tyler collects 1242 cans of pet food. He gives 150 cans to the vet. Then he packs 9 cans in each box to give to the animal shelter. How many cans of pet food are not in a box?
Answer:
121
Step-by-step explanation:
1242-150=1092/9 = 121 (remainder 3)
Answer: 121
Step-by-step explanation: 1241 - 150 / 9
Write a similarity transformation that maps ∆ABC to ∆DEF
Answer:
Reflect ABC over the y axis. Translate ABC 1 unit to the right. C is the center, dilate ABC with a scale factor of 2.
Step-by-step explanation:
