Consequently, the solution of the given question of probability comes out to be P(x<5.67 = 0.63
What is probability?Probability fundamentals. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Here,
we use the z-score algorithm to answer this query.
Score Z = x - 40/5
x = the raw score
population mean= μ
Population standard deviation is σ
Hence,
x = 40 μ = 5.67, σ =5
Z = 5.67 - 40/5
z=0.37
Probability based on the Z-Table:
P(x<5.67 = 0.63
Consequently, the solution of the given question of probability comes out to be P(x<5.67 = 0.63 .
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Which variation is represented by this situation:
Martha earns $375 when she works 5 hours. How much will she earn
if she works 12 hours? Is it direct variation or inverse variation?
Direct variation is represented by this situation and she earn $900
if she works 12 hours.
What are direct variation and indirect variation?Direct variation describes a relationship whereby one measure directly affects the other when the first one changes. This is completely opposed by inverse variation. Learn the definitions of direct and inverse variations in this article, along with some instances that have been solved.
How do inverse and direct variations differ from one another?When x is not equal to 0, y = kx is the equation that describes the linear function known as direct variation. An equation of the form xy = k, where x is not equal to zero and k is a nonzero real number constant, describes the nonlinear function known as inverse variation.
5 hours = earns $ 375
1 hours = 375/5 = earns $ 75
12 hours = 75 12 = earns $ 900
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a sample of a radioactive isotope had an inital mass of 130 mg in the year 2010 and decays exponentially over time. a measurmentin the year 2012 found that the samples masshad decayed to 80 mgwjat would be the expected mass of the sample in the year 2021 to the nearest whole number
The expected mass of the sample in the year of 2021 is given as follows:
9 mg.
How to define the exponential function?An exponential function is defined as follows:
y = a(b)^x.
For which the parameters are given as follows:
a is the initial value.b is the rate of change.The initial mass was of 130 mg, hence the parameter a is given as follows:
a = 130.
In two years, the mass decayed to 80 grams, hence the parameter b can be obtained as follows:
b² = 80/130
b = square root(80/130)
b = 0.78446454055.
This means that the exponential function for the mass of the sample in x years after 2010 is given as follows:
y = 130(0.78446454055)^x.
2021 is 11 years after 2010, hence the expected mass is obtained as follows:
y = 130(0.78446454055)^11
y = 9 mg.
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-8 5/9 = 4 2/3w
.............................
Answer:
w = -11/6
Step-by-step explanation:
-8 5/9 = 4 2/3w
-8 5/9 = -77/9
4 2/3 = 14/3
So, our equation is
-77/9 = 14/3w
Divided both sides by 14/3
w = -11/6
find the values of x, z and y
The values of x is 82° , z is 98°and y is 69°. in the given triangle.
Is the sum of all triangle angles always 180 degrees?Because one outside angle of a triangle is equal to the total of the other two angles in the triangle, the angles of a triangle add up to 180 degrees. In other words, the third angle must join with the other two angles in the triangle to generate a 180-degree angle (the two angles that add up to form the outside angle).
we know that the sum of angle of triangle = 180
so,
x+ 60 +38=180
x=180-8
x=82°
and also
x+z = 180
z= 98°
for value of y
13 + 98 +y = 180
y= 69°
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Evaluating Linear Functions
The value of linear equations are f(x) = -17 and f(x) = -73 .
What is linear equation ?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).
Equation with two variables of degree one is referred to as a linear equation with two variables. Formal expression: ax+by+c=0, where a, b, c R & a, b 0.
A)
f(x) = -2x + 7 when x = -12f (x) = -2*12 + 7
= -24 + 7
= -17
f(x) = 5x - 13 when x = -14f(x) = 5*-14 - 13
= -60 -13
= -73
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if pam makes 250 dollars from making 15 pots, what is her piece rate?
Pam's piece rate is $16.67 for every pot she produces.
What is the rate?A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.
Pam's piece rate is the amount of money she earns for each pot she makes. In this case, she earned $250 for making 15 pots, so her piece rate is:
$250 ÷ 15 pots = $16.67 per pot
Therefore, Pam earns $16.67 for each pot she makes. This is a way of calculating her pay based on the number of units she produces, rather than by the hour.
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Please help I have a learning disablity and need help with this.
Please answer both parts
Find the product mentally. Show the steps you used.
4 x 5 1/8
Which one is correct
4(5) + 4 (1/8)
20 + 1/8
4 + 5 (1/8)
4 + 41/8
Answer here _______________
Find the product in the simplest form. Use your answer from question 1 when we rewrote it using the Distributive Property.
4 x 5 1/8
20 1/8
20 1/2
20/8
2 1/4
Answer here ______________
The product value of 4 x 5(1/8) is 4(5) + 4(1/8).
Option A is the correct answer.
The product value of 4 x 5(1/8) is 20(1/2).
Option B is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
4 x 5(1/8)
= 4 x (5 + 1/8)
= 4 x 5 + 4 x 1/8
4 x 5(1/8)
= 4 x (5 + 1/8)
= 4 x 5 + 4 x 1/8
= 20 + 1/2
= 20(1/2)
Thus,
4(5) + 4 (1/8) is the value.
20(1/8) is the value.
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An equilateral triangle $ABC$ shares a common side $BC$ with a square $BCDE,$ as pictured. What is the number of degrees in $\angle DAE$ (not pictured)
30° = angle DAE
Step-by-step explanation:
We have ACD with angle ACD = 150°, and because CD = CA, angle CAD and ADC are equal, so angle CAD = [180 -150] / 2 = 30/2 = 15°.
if we draw AE in ABE using the same process, angle EAB = 15°,
so CAB = 60° = angle =CAD + angle DAE + angle EAB
60 = 15 + angle DAE + 15
60 = 30 + angle DAE
30° = angle DAE
Triangle with an equilateral shape. An equilateral triangle is a triangle with all of its sides being the same length. An equilateral triangle, for example, has three sides equal to 5cm. Because the three sides are equal, the three angles opposite the equal sides are equal in size.
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What Is 8 1/8 - 4 3/8
Answer:
3 3/4 or 3 6/8
Step-by-step explanation:
hope this helps <3
b) Is Jerome’s brother correct? Explain why or why not, using examples from the ratio table to support your argument.
Answer:
i wish i could help im sorry
Step-by-step explanation:
im
not
ok
At which points are the equations y = x2 3x 2 and y = 2x 3 approximately equal?
The quadratic equations are approximately equals at the points (0.618,4.236) and (-1.618 , -0.236)
What in mathematics is a quadratic equation?
A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.
The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem.
we have
y = x² + 3x + 2 .............(a)
y = 2x + 3 ...................(b)
To solve the system of equations equate equation A to equation B
x² + 3x + 2 = 2x + 3
Group terms that contain the same variable
x² + 3x + 2 - 2x - 3 = 0
x² + x - 1 = 0
The formula to solve a quadratic equation of the form ax² + bx+ c is equal to
in this problem we have
x² + x - 1 =0
so, a= 1
b = 1
c = -1
substitute in the formula
x = -1 ± √1² - 4(1)(-1)/2(1)
x = -1 ±√5/2
x = -1+√5/2 = 0.618
x = -1 - √5/2 = - 1.618
Find the values of y
for x = 0.618
y = 2(0.618) + 3 = 4.236
for x = - 1.618
y = 2(-1.618) + 3 = -0.236
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The complete question is -
At which points are the equations y = x2 + 3x + 2 and y = 2x + 3 approximately equal?
what part of 3$ is the sum of 7 dimes, 1 nickel and 3 pennies?
Answer:
7/60
Step-by-step explanation:
First, we would need to add up all of the coins and know their values.
1 dime (d) = 10¢
1 nickel (n) = 5¢
1 penny (p) = 1¢
An equation we can use will look something like this:
(d × 7) + (n × 1) + (p × 3) =?
Now just add the numbers and solve.
(10 × 7) + (5 × 1) + (1 × 3) = 78
Therefore, the total amount is 78¢.
Now to figure out how much 78¢ is out of $3, we can use an equation that looks something like this:
3 ÷ 0.78 = 3.84615385 or 7/60
So, this means that with 7 dimes, 1 nickel and 3 pennies it is 7/60 of $3.
1. Marta walked 6 miles in 1.5 hours. At this rate how long will it take her to walk 16 miles?
2. Lionel typed 320 words in 4 minutes. At this rate, how long will it take him to type 800 words?
Answer for no.2: 800
Step-by-step explanation:
Of the 6,960 balloons thrown in a water-ballon fight, 870 were red. At this rate, how many balloons out of 48 would be red? WRITE JUST THE ANSWER WITHOUT UNITS
At this rate, the ratio or proportion of red balloons to the total balloons, the number of red balloons out of 48 is 6.
What is proportion?Proportion describes the two or more ratios equated to each other.
Proportions are depicted as fractional values in decimals, fractions, or percentages.
In this situation, we equate the ratio or proportion of red balloons to the sample to determine the number that will likely be red.
The total number of balloons thrown in a water balloon fight = 6,960
The number of the balloons that are red = 870
The proportion of the red balloons to the total = 0.125 or 12.5% (870/6,960)
In a sample of 48 balloons, the number of red balloons will be 6 (48 x 0.125)
Thus, out of 48 balloons, there are 6 red balloons at this constant rate.
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How many dollars will Ms. Davis have saved after 30 weeks?
Ms. Davis has $54. 50 saved
• She will save $33. 25 each week for the next 30 weeks
• She will not spend any of the money
Enter your response here:
$1052 is the total saving og Ms. Davis after 30 weeks from the given point .
Given that:
Inital saving of Ms. Davis = $54.50
Ms. Davis has already saved $54.50 and plans to save an additional $33.25 each week for the next 30 weeks. This means that she will be adding a total of $33.25 x 30 = $997.50 to her savings over the next 30 weeks.
If she does not spend any of the money she has saved, her total savings will be :
sum of Initial saving and saving after 30 weeks
$54.50 + $997.50 = $1,052.00.
so the total saving is $1052.
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g(n)=-3n-4; Find g(-8)
Answer:
g(- 8) = 20
Step-by-step explanation:
substitute x = - 8 into g(x) , that is
g(- 8) = - 3(- 8) - 4 = 24 - 4 = 20
There are 260 eighth grade students at South Whitenardh middle school. All right grade students are required to enroll in either a music class or an art class. No students take both art and music classes. The number of students taking music classes is 14 more than twice the number taking art classes. Write an equation to represent the total number of eight grade students
178 students taking a music class and 82 students taking an art class
There was no clear question, but I'm assuming you want to know how many students are enrolled in music and painting classes.
Let x= the number of children enrolled in art classes.
number of children enrolled in music classes: 2x + 14
The overall number of children will be 260, including all of these children.
x+2x+14 = 260
3x=246 x=82 pupils attend an art lesson.
To find people taking music classes, enter x to 2x+14.
2(82)+14 = 178
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The complete question would be;
There are 260 eighth-grade students at South Whitemarsh Middle School. All eighth-grade students are required to enroll in either a music class or an art class. No students take both art and music classes. The number of students taking music classes is 14 more than twice the number taking art classes.
Lara says that she can use this picture to show that two pairs of congruent angles and one pair of corresponding congruent sides is enough information to prove that two triangles are congruent. Is Lara correct
Yes, the information provided regarding the two pairs of congruent angles so one pair with corresponding congruent sides is sufficient to demonstrate the congruence of two triangles.
Define the term congruent triangles?Congruent refers to things that are exactly the same size and shape.
When a triangle has precisely the same sides and precisely the same three angles, it is said to be congruent.These triangles are congruent if two pairs of comparable angles and the pairs of included sides are also congruent. The triangles are congruent if two pairs with corresponding angles and just a pair of non-included sides also are congruent.For the stated question-
The following are the steps:
Due to a sequence of stiff motions, the triangles will line up precisely.Additionally, Lara is right only if the matching congruent side is situated halfway between the two angles.Angle Side Angle Congruceny, or "ASA" triangle congruceny, would be the case here.Thus, the information provided regarding the two pairs of congruent angles so one pair with corresponding congruent sides is sufficient to demonstrate the congruence of two triangles.
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Select the correct answer. A body travels 10 meters during the first 5 seconds of its travel, and it travels a total of 30 meters over the first 10 seconds of its travel. What is its average speed during the time from t
The speed of travel will be 4 m/s.
How do you find the distance traveled in the Nth second?The formula for distance travelled in nth second is given by, Sn = u + a (n – ½).
The body's total distance travelled is equal to the sum of the 10 m it covered in the first five seconds and the 30 m it covered in the following five seconds. The total distance covered is 40 metres. This can be divided by the duration to determine the average speed. Therefore, the average speed is 4 m/s.
Total distance=10+30=40
speed=distance/time=40/10=4m/s
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0.5- 2 2/5 = 1/2y +2.4 Please help! Find the value of y! Thanks!
The value of y, given the equation, can be found to be - 8 .6
How to find the value of y ?To find the value of y, first convert the mixed fraction to a decimal for easier calculation :
2 ² / ₅ = 2 + 2 / 5
= 2 + 0. 4
= 2. 4
The equation then becomes :
0. 5 - 2.4 = 1 / 2 y + 2. 4
This can be rewritten as :
0. 5 - 2.4 = 1 / 2 y + 2. 4
0. 5 - 2 . 4 - 2. 4 = 1 / 2 y
1 / 2 y = - 4. 3
y = - 4. 3 / 1 / 2
y = - 8 .6
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Pleaseeee help asapppppp
Simplifying
0.75x + 1.2 = 0
Reorder the terms:
1.2 + 0.75x = 0
Solving
1.2 + 0.75x = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-1.2' to each side of the equation.
1.2 + -1.2 + 0.75x = 0 + -1.2
Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 0.75x = 0 + -1.2
0.75x = 0 + -1.2
Combine like terms: 0 + -1.2 = -1.2
0.75x = -1.2
Divide each side by '0.75'.
x = -1.6
Use the diagram to find.. (Trigonometry)
Answer:
Step-by-step explanation:
b and f
What is the coefficient of x² in 3x 5?
The coefficient of the variable x² in the expression 3x+5 is 0
Given that,
The expression is 3x+5
To find : The coefficient of the variable x² in the expression
Coefficient is the number that is beside the variable in the equation.
The coefficient of x in 3x+5 is 0
A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6
As we can see that the term that is in multiplication with x² is 3.
Hence, the coefficient of x² in the equation 3x+5 is 0.
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What are the 7 steps in problem solving examples?
The 7 stepd in problem-solving examples are:
Step 1: Read through the problem
Step 2: Draw diagram
Step 3: Assign variable to each unknown
Step 4: Translate information into an equation
Step 5: Check the equation
Step 6: Use algebra rules to solve the equations
Step 7: Check the final answer.
We know that the word problems are required to translate the real world problem into mathematical terms.
Everything mentioned in the word problem is important.
The seven necessary steps in problem solving examples:
Step 1: Read the problem throughly
Step 2: Draw picture / diagram / arrow diagram related to example
Step 3: Assign an alphabate to each unknown value
Step 4: Translate information into an equation
Step 5: Check the types equation
Step 6: solve the equations using algebra rules
Step 7: Check the final answer.
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1
Which line is pointing to the cell body?
A. 1
B. 2
C. 4
D. 5
2
3
4
5
Image by Dhp 1080
The line 2 is pointing towards the body of the cell, in the given image of a neuron.
What is cell body?The soma, or cell body, is the spherical part of the neuron that houses the nucleus. The cell body is linked to the dendrites, which transport information to the neuron, and the axon, which sends information to other neurons.
When one neuron receives information from another, the dendrites send it to the cell body. Depending on the signal strength, the cell body may then send the information to the axon.
The cell body's role is to regulate all of the cell's functions. It has several important organelles that aid in this process. Organelles are tiny organelles found within cells that each perform a specific function. The nucleus is the most important organelle within the cell body.
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Andy and Trevor share 40 sweets in a ratio 11: 9
How many more sweets does Andy receive than Trevor does?
Answer:
Step-by-step explanation:
no
Answer:
22:18
Step-by-step explanation:
In this case, firstly you have to add 11 and 9 together, which makes 20.
Then, 40 ( number of sweets ), divided by 20 gives us 2.
This means that every piece, or block, of our ratio will be 2.
Therefore, the last step is multiplying 11x2 and 9x2.
So, Andy has 22 sweets an Trevor has 18.
n \triangle NOP,△NOP, \overline{PN}\cong \overline{OP}
PN
≅
OP
and \text{m}\angle P = 50^{\circ}.m∠P=50
∘
. Find \text{m}\angle O.m∠O.
The value of the measure of ∠O in the given triangle will be 65°
What is triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In ΔNOP;
PN ≅ OP
So, ∠O = ∠N
And, Measure of ∠P = 50°
Now,
In the ΔNOP;
The sum of all the three angles are 180°.
The value of the measure of ∠O = x
We get;
∠O + ∠N + ∠P = 180°
Substitute ∠P = 50° and ∠O = ∠N = x we get;
x + x + 50 = 180
2x + 50 = 180
2x = 180 - 50
2x = 130
x = 65
Thus, The value of the measure of ∠O will be 65°.
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Find out the answer to 4x+12=63
[tex]12 \frac{3}{4} [/tex]
or 12.75
Answer:
x=12.75
Step-by-step explanation:
Follow the steps within the image.
-Hope this helped
Rene makes $38,000 per year and pays about 35% of
his gross monthly income in federal and state taxes.
He wants to find an apartment to rent. Estimate how
much he can afford to pay for rent each month. Then
determine how much money he will have after taxes
and rent are paid.
PLEASE HELP
After the taxes and rent, the remaining amount in his gross pay is $5,700
The term gross income is defined as also known as gross pay when it’s on a paycheck is an individual’s total earnings before taxes or other deductions.
Here we have given that Rene makes $38,000 per year and pays about 35% of his gross monthly income in federal and state taxes.
And as we all know that If you live in a metropolitan city, your HRA is equivalent to 50% of your basic salary.
Therefore, the remaining amount in his hand is calculated as,
=> $38000 - [35% of income + 50% of income]
Here the 35% of income is
=> 38000 x 35/100
=> 380 x 35
=> 13300
Similarly, the 50 percent of the income is
=> 38000 x 50/100
=> 380 x 50
=> 19000
Then the remaining amount is calculated by apply the values on it, then we get,
=> $38000 - [$13300 + $19000]
=> $3800 - $32300
=> $5700
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Write and solve an equation to find what fraction of the student f voted for fruit juice or water
If [tex]\frac{1}{4}[/tex] of fruit punch is pineapple juice. About [tex]\frac{1}{6}[/tex] of the fruit punch is orange juice, then fraction of punch that is pineapple juice or orange juice is [tex]\frac{5}{12}[/tex] .
The fraction of pineapple juice in fruit punch is = [tex]\frac{1}{4}[/tex] ;
the fraction of orange juice in fruit punch is = [tex]\frac{1}{6}[/tex] ;
the equation that can be used to find the fraction of fruit punch that is pineapple juice or orange juice is
⇒ [tex]Frcation Of (Pinapple Juice +Orange Juice)[/tex]
substituting the values ,
we get the equation as ;
⇒ [tex]\frac{1}{4} +\frac{1}{6}[/tex]
taking LCM as 4 and 6 as 12 and solving further ,
we get ;
⇒ [tex]\frac{3}{12} +\frac{2}{12}[/tex] ; = [tex]\frac{5}{12}[/tex] .
Therefore , the fraction of fruit punch that is pineapple juice or orange juice is [tex]\frac{5}{12}[/tex] .
The given question is incomplete , the complete question is
About 1/4 of fruit punch is pineapple juice. About 1/6 of the fruit punch is orange juice. Write and solve an equation to find the fraction of the punch that is pineapple juice or orange juice .
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