The estimated value of the variable x is 8. 24
How to determine the valueit is important that we know algebraic expressions are expressions with terms, coefficients, variables, constants and factors.
They are also expressions with mathematical expressions.
From the information given, we have that;
8.9(x – 4.2) = 35.99
Now, divide both sides by 8.9, we get;
x - 4. 2 = 4. 04
collect the like terms, we have;
x = 4. 04 + 4.2
Add the collected like terms, we have;
x = 8. 24
Hence, we can say that the student's solution was incorrect and the value is 8.24
Learn about linear equations on:
https://brainly.com/question/2030026
#SPJ1
10-2 eeaaasadaddadeeee
Answer:thwe answer is 8
Step-by-step explanation:
Answer:88
Step-by-step explanation:
Anand just accepted a job at a new company where he will make an annual salary of $60000. Anand was told that for each year he stays with the company, he will be given a salary raise of $2000. How much would Anand make as a salary after 10 years working for the company? What would be his salary after � t years?
Answer: Anand's salary after 10 years working for the company can be calculated as follows:
$60000 + $2000 * 10 = $60000 + $20000 = $80000.
To determine Anand's salary after t years working for the company, we can use the following formula:
$60000 + $2000 * t
So, if t is the number of years he has worked for the company, his salary after t years would be:
$60000 + $2000 * t.
Step-by-step explanation:
Simplify
1.1. 4 x 5a + 3a x-6
1.2. 6ab+2b-16a+ (-2)
1.3. 1024000: 360000:180000
1.4. 150 min: 3 hours
The values of the expression following the collection of like terms, rearranging and factoring are presented as follows;
1.1 4·x + 5·a + 3·a + x - 6 = 5·x + 8·a - 6
1.2. 6·a·b + 2·b - 16·a - 2 = 2·(3·a·b + b - 8·a - 1)
1.3. 1024000 : 360000 : 180000 = 256 : 90 : 45
1.4. 150 min : 3 hours = 5 : 6
What is a mathematical expression?A mathematical expression comprises of mathematical symbols, numbers and variable, properly arranged to represent a value.
The simplification of the expressions can be presented as follows;
1.1. 4·x + 5·a + 3·a + (x - 6)
The terms in the above expression can be rearranged as follows;
4·x + 5·a + 3·a + (x - 6) = 4·x + x + 5·a + 3·a - 6
4·x + x + 5·a + 3·a - 6 = 5·x + 8·a - 6
Therefore, whereby the expression in the question is; 4·x + 5·a + 3·a + (x - 6), we get;
4·x + 5·a + 3·a + (x - 6) = 5·x + 8·a - 61.2. Whereby the possible expression in the question is; 6·a·b + 2·b - 16·a + (-2), we get;
The factor common to the terms of the expression 6·a·b + 2·b - 16·a + (-2) is 2. Therefore by factoring the expression, we get;
6·a·b + 2·b - 16·a + (-2) = 3·(a·b + b - 8·a - 1)1.3. 1024000: 360,000 : 180,000
The expression is a ratio of the form a : b : c
Dividing each term in the ratio by 1,000, we get
1024000 ÷ 1000 : 360,000 ÷ 1000 : 180,000 ÷ 1000 = 1024 : 360 : 180
1024000: 360,000 : 180,000 = 1024 : 360 : 180
The common factors of 1024, 360 and 180 are; 1, 2, and 4
Therefore, the GCF of 1024, 360, and 180 is 4
Dividing the terms of the ratio 1024 : 360 : 180 by 4, we get;
1024 ÷ 4 : 360 ÷ 4 : 180 ÷ 4 = 256 : 90 : 45
Therefore;
1024000: 360,000 : 180,000 = 256 : 90 : 451.4 150 min : 3 hours
The above ratio can be simplified by rewriting the ratio using unit conversion as follows;
3 hours = 180 minutes, therefore;
150 min : 3 hours = 150 min : 180 min
150 : 180 = 5 : 6
Therefore; 150 min : 180 min = 5 min : 6 min
150 min : 3 hours = 5 : 6Learn more on ratios here: https://brainly.com/question/29426345
#SPJ1
For the following exercises, line L is given.
a. Find point P that belongs to the line and direction vector v of the line. Express v in component form.
b. Find the distance from the origin to line -x=y+1, z=2
a. Point P on the line and the direction vector v of the line can be expressed as P = (x0, y0, z0) + t(a, b, c).
b. The distance from the origin to the line -x=y+1, z=2 is the shortest distance between a point and a line.
Here (x0, y0, z0) is a point on the line and (a, b, c) is the direction vector. To find (x0, y0, z0) and (a, b, c), we need more information about the line.
This formula involves taking the dot product of the direction vector of the line and the difference between a point on the line and the origin. Again, we need more information about the line in order to calculate this distance.
Without more information about line L, it is not possible to find the point P or the distance from the origin to the line.
Learn more about Line:
https://brainly.com/question/18831322
#SPJ4
Bashir has a toy car collection. He keeps some in display case and the rest on the wall. 136 of his toys are on the wall and 15% of the toys are in the display what is the total number of toys in barshirs collection
The total number of toys in Bashir's collection is 160.
How to find the total number of toys in Bashir's collection?
A percentage is a number or ratio that can be expressed as a fraction of 100.
Let N represent the total number of toys in Bashir's collection
Since 136 of his toys are on the wall and 15% of the toys are in the display. We can write:
136 + (15% of N) = N
136 + (15/100 * N) = N
136 + 0.15N = N
N - 0.15N = 136
0.85N = 136
N = 136/0.85
N = 160
Learn more about percentages on:
brainly.com/question/843074
#SPJ1
is this relation a function?
Answer:
Step-by-step explanation:
the green one no
the red ones yes
The radius of the circle below is 21 mm.
Calculate the area of the circle.
Give your answer in mm² to 1 d. p.
21 mm
Answer:The area of a circle can be calculated using the formula:
A = πr²
where A is the area and r is the radius.
Plugging in the given radius of 21 mm, we get:
A = π * 21² = π * 441
A = 441π mm²
To 1 decimal place, 441π can be approximated to 1393.1 mm². So, the area of the circle with a radius of 21 mm is approximately 1393.1 mm² to 1 decimal place.
Step-by-step explanation:
factoriser 30x²-11x-6
Answer:
x=2/3 or x= -3/10
Step-by-step explanation:
30x²-11x-6=0
ax²+bx+c=0
30x²+9x-20x-6=0
3x(10x+3)-2(10x+3)=0
(3x-2)(10x+3)=0
3x-2=0 or 10x+3=0
3x=2 or 10x= -3
x=2/3 or x= -3/10
Gallons of water in an area of .5 x 2 x 55 ft
Answer: It´s about 14.96 gallons per square foot with 55 square foot area and 2 feet height
Step-by-step explanation:
The letters of EAGLES should be evenly spaced across a 61-inch-wide banner, with no margins. Each letter is 6 inches wide. How many inches should exist between each pair of letters
The distance between each pair of letters in the word is given by the equation A = 5 inches
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the distance between each pair of letters be A
Now , the equation will be
Let the total distance of the wide banner be = 61 inches
Now , the word is given by { E , A , G , L , E , S }
The number of letters in the word = 6 letters
The width of each letter = 6 inches
So , the total length of all the letters = 6 x 6 = 36 inches
The remaining distance in the wide banner = total distance of the wide banner - total length of all the letters
On simplifying the equation , we get
The remaining distance in the wide banner = 61 - 36
The remaining distance in the wide banner = 25 inches
Now ,
The distance between each pair of letters = remaining distance in the wide banner / 5 spaces
On simplifying the equation , we get
The distance between each pair of letters A = 25 / 5
The distance between each pair of letters A = 5 inches
Hence , the equation is A = 5 inches
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
HELP ME PLEASE!
Daniel is painting the 3 walls of his bedroom that do not have a door. He knows that the measurement of the height of each wall is 78 inches and that 1 gallon of paint will cover 300 square feet of wall space. How many gallons of paint will Daniel need?
The number of Gallons of paint that Daniel will need is; 3 gallons
How to solve Algebra Word problems?The parameters given are;
Height of each wall = 78 inches = 78/12 = 6.5 ft
Length of wall 1 = 7 ft
Length of wall 2 = 6 ft
Length of wall 3 = 7 ft
Area of wall 1 = 6.5 * 7 = 45.5 sq.ft
Area of wall 2 = 6.5 * 6 = 39 sq.ft
Area of wall 3 = 6.5 * 7 = 45.5 sq.ft
Total area = 45.5 + 45.5 + 39
= 130 sq.ft
1 gallon of paint will cover 300 square feet of wall space
Number of gallons required = 300/130
= 2.3 gallons
Approximating to a whole number gives 3 gallons
Read more about Algebra Word Problems at; https://brainly.com/question/21405634
#SPJ1
How can I find the area under the normal distribution between z= -0.30 and z=0.90?
To find the area under the normal distribution between z = -0.30 and z = 0.90, you can use a standard normal distribution table or a calculator with a normal distribution function.
Using a standard normal distribution table:
Look up the area to the left of z = 0.90 in the standard normal distribution table. This will give you a value of 0.8159.
Look up the area to the left of z = -0.30 in the standard normal distribution table. This will give you a value of 0.3821.
Subtract the value from Step 2 from the value from Step 1 to find the area between z = -0.30 and z = 0.90:
Area = 0.8159 - 0.3821 = 0.4338
Using a calculator with a normal distribution function:
Use the normal distribution function on your calculator with a mean of 0 and a standard deviation of 1 to find the area to the left of z = 0.90. This will give you a value of 0.8159.
Use the normal distribution function on your calculator with a mean of 0 and a standard deviation of 1 to find the area to the left of z = -0.30. This will give you a value of 0.3821.
Subtract the value from Step 2 from the value from Step 1 to find the area between z = -0.30 and z = 0.90:
Area = 0.8159 - 0.3821 = 0.4338
Therefore, the area under the normal distribution between z = -0.30 and z = 0.90 is 0.4338.
A pool measuring 16 meters by 28 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 864 square meters, what is the width of the path?
Let the width of the path be represented by x.
The total width of the pool and the path would then be 16 + 2x (for the two shorter sides) and 28 + 2x (for the two longer sides).
The area of the pool itself is 16 × 28 = 448 square meters.
The area of the combined pool and path is 864 square meters.
So the area of just the path is:
864 - 448 = 416 square meters
The area of the path can also be expressed as the area of the larger rectangle (16 + 2x) × (28 + 2x) minus the area of the pool (16 × 28).
So we can set up the equation:
(16 + 2x) × (28 + 2x) - 448 = 416
Expanding the left side and simplifying:
4x^2 + 88x - 480 = 0
Dividing by 4:
x^2 + 22x - 120 = 0
Using the quadratic formula:
x = (-22 ± sqrt(22^2 - 4(-120)))/2
x = (-22 ± 26)/2
x = 2 or x = -24
The width of the path cannot be negative, so the width of the path is 2 meters.
Solve for the truth table:
Due to length restrictions, we kindly invite to see the explanation below to know the complete truth table of the composite proposition.
How to complete a truth valueAccording to logics, propositions are constructions that contains a truth value and in this question we must complete a truth value of a composite proposition, that is, a combination of simpler proposition.
To complete a this table, we must begin with the most simple proposition and go through propositions with more complexity:
p q r ¬ p ¬ q p → q r ∧ ¬ p r ∨ ¬ q
T T T F F T F T
T T F F F T F F
T F T F T F F T
F T T T F T T F
F F T T T T T T
F T F T F T F F
F F F T T T F F
[(p → q) ∨ (r ∧ ¬ p)] [(p → q) ∨ (r ∧ ¬ p)] → (r ∨ ¬ q)
T T
T F
F T
T F
T T
T F
T F
To learn more on truth tables: https://brainly.com/question/27989881
#SPJ1
5. If A=4 and B=6, then what is 6A plus 3B?
Answer:
42
Step-by-step explanation:
6*4+3*6= 42
Answer:
42
Step-by-step explanation:
6*4+3*6=42
A family drove a distance of 354 miles in 5 hours about how many miles did they travel each hour
Answer:
An average of 70.8 miles per hour
Step-by-step explanation:
Cigarette Taxes The data shown represent the
cigarette tax (in cents) for 50 selected states. Check
for normality.
The range of the cigarette tax (in cents) for 50 selected states is 62.
What is range?The range of a function is defined as the set of all the possible output values that are valid for the given function.
The range of a given set of data is the difference between the largest value and the smallest value.
Given the data shown represent the cigarette tax (in cents) for 50 selected states
70,12,42,45,50,51,60,69,8,40,18
Required; The range
This is calculated as:
Range = highest - lowest
Range = 70 - 8
Range = 62
Learn more about range of the function:
brainly.com/question/2264373
#SPJ1
A building casts a shadow 5 ft long. At the same time, the shadow cast by a vertical yardstick is 5 ft long. How tall is the building?
Answer: Let's call the height of the building "h".
The length of the shadow cast by the building is 5 feet, and the length of the shadow cast by the yardstick is also 5 feet. This means that the ratio of the height of the building to the length of its shadow is the same as the ratio of the height of the yardstick to the length of its shadow.
h / 5 = 1 / 5
Cross-multiplying, we get:
h = 5 * 1 / 5
h = 1
So the building is 1 foot tall.
Step-by-step explanation:
Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-unit production run in the following situations.
(a) The process standard deviation is 0.25, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.75 or greater than 10.25 ounces will be classified as defects. If required, round your answer for the probability of a defect to four decimal places and for the number of defects to the nearest whole number.
Probability of a defect:
Number of defects:
The probability of a defect is 5.7330 x [tex]10^{-5}[/tex] and the number of defects is 5.73.
To calculate the probability of a defect, we need to find the area under the standard normal curve that lies outside of the process control limits of 9.75 ounces and 10.25 ounces. We can use the standard normal distribution table to find this area.
First, we need to standardize the weight limits as follows -
[tex]Z_{lower}[/tex] = (9.75 - 10) / 0.25 = -4
[tex]Z_{upper}[/tex] = (10.25 - 10) / 0.25 = 4
Next, we will find the area under the standard normal curve that lies outside of these limits as follows -
P(Defect) = P(Z < -4) + P(Z > 4)
Using a standard normal distribution table, we can find that P(Z < -4) = 2.8665 x [tex]10^{-5}[/tex] and P(Z > 4) = 2.8665 x [tex]10^{-5}[/tex] .
So, the total probability of a defect is -
P(Defect) = 2.8665 x [tex]10^{-5}[/tex] + 2.8665 x [tex]10^{-5}[/tex] = 5.7330 x [tex]10^{-5}[/tex]
Finally, we will find the number of defects for a 1,000-unit production run as follows -
The number of defects = 1000 * 5.7330 x [tex]10^{-5}[/tex] = 5.73 (rounded to the nearest whole number).
Read more about Probability:
brainly.com/question/24756209
#SPJ4
express as a torinomial (2x-4)(x+8)
Answer:
2x²+12x-32
Step-by-step explanation:
An endangered species has 400 animals left in the wild. If the species is decreasing by 6.5% each year, how many animals are left after 4 years?
The number of animals left in the wild after 4 years is approximately 306.
What is Compound Interest?Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.
We are using the concept of compound interest to solve the given problem.
The formula to find the final amount in compound interest is,
A = P (1 + r) ^t
Here P = 400
r = -6.5% = -0.065 (negative sign because the rate is decreasing)
t = 4 years
Substituting the values,
A =400 (1 - 0.065)⁴
= 305.71 ≈ 306
Hence there will be 306 animals left in the wild after 4 years.
Learn more about Compound Interest here :
https://brainly.com/question/13155407
#SPJ1
It’s number 5 I need the answer for it
The relationship between x and y is y = x + 2
The plot of the points and the straight lineFrom the question, we have the following parameters that can be used in our computation:
(1, 3), (2, 4), (3, 5) and (5, 7)
See attachment for the line
Using the above as a guide, we have the following:
The three other points are (6, 8), (7, 9) and (8, 10)
The relationship between x and yFrom the ordered pairs, we can see that
y is the sum of x and 2
This means that
y = x + 2
Read more about linear relations at
https://brainly.com/question/30318449
#SPJ1
HELP ASAP! TELL ME THE CODE TO THIS, I DIDNT FORGET THE PICTURE THIS TIME
The area of the composite shapes found using the formula for the area of a rectangle and the perimeter of the figure indicates that the solution to the puzzle is; AGIH
What is the area of a rectangle?The area of a rectangle = The length of the rectangle × The width of the rectangle
The area and perimeter of the shapes can be found by considering the shapes as composite figures as follows;
Area of shape 1 = Area of the 8 by 5 rectangle - Area of the 2 by 2 square at the top middle portion
Therefore;
The area of shape 1 = 8 cm × 5 cm - 2 cm × 2 cm = 36 cm²Perimeter of shape 1 = 8 cm + 5 cm + 3 cm + 2 cm + 2 cm + 2 cm + 3 cm + 5 cm = 30 cmThe area of shape 2 = Area of the 13 by 4 rectangle - Area of the 2 by 3 rectangle at the top middle part of the shape.
(The width of the open part at the top of the rectangle is (13 cm - 2 × 5 cm) = 3 cm)
Area of shape 2 = 13 cm × 4 cm - (13 cm - 2 × 5 cm) × 2 cm) = 46 cm²The perimeter of shape 2 = 13 cm + 4 cm + 5 cm + 2 cm + (13 cm - 2 × 5 cm) + 2 cm + 5 cm + 4 cm = 38 cmThe four letter code is therefore;
AGIH
Learn more on the area and perimeter of composite figures here: https://brainly.com/question/29045691
#SPJ1
Which type of wave is most affected by gravity from the Sun and the moon?(1 point)
Responses
water
water
electromagnetic
electromagnetic
sound
sound
seismic
Answer:A tidal wave is a regularly reoccurring shallow water wave caused by effects of the gravitational interactions between the Sun, Moon, and Earth on the ocean.
Strategy-planning activity in which top management envisions different what if scenarios to anticipate plausible futures in order to derive strategic responses is definition of ?
Strategy-planning activity in which top management envisions different what if scenarios to anticipate plausible futures in order to derive strategic responses is definition of: Scenario planning.
What is Scenario planning?Scenario planning gives company decision-makers the ability to assess reactions, manage for both good and negative possibilities, and establish ranges of prospective outcomes and anticipated implications. Scenario planning is more than simply a financial planning tool; it's an integrated strategy for coping with uncertainty. It includes predicting financial results, calculating cash flow, and devising mitigation actions. But it goes beyond only being a means to identify and reduce risk or prepare for growth scenarios. Planning scenarios involves imagining several futures for an organisation based on various, sometimes positive, sometimes negative, assumptions about market dynamics. Scenario planning is a method pioneered by the United States military, which now conducts exercises looking up to 20 years in advance to direct R&D activities.
To know more about Strategy-planning activity refer to:
https://brainly.com/question/24864915
#SPJ4
highest common factor 84,126 245
Answer: 7 is the common factor for ALL of these numbers.
For each of the following, determine the constant c so that f(x) satisfies the conditions of being a pmf for a random variable X, and then depict each pmf as a line graph: a. f(x) = x/c, x = 1, 2, 3, 4. b. f(x) = cx, x = 1, 2, 3, ... , 10. c.
f(x)=c(1/4)^x , x = 1, 2, 3, . ... d. f(x) = c(x + 1)², x = 0, 1, 2, 3. e. f(x) = x/c, x = 1, 2, 3, ... , n. f. f(x) = c/(x + 1) (x + 2), = 0, 1, 2, 3, ... . Hint: In part (f), write f(x) = 1/(x + 1) − 1/(x + 2).
For each of the functions, the constant c was determined so that the function would satisfy the conditions of being a pmf for a random variable X, and then a line graph was plotted for each pmf.
a. c = 4 so that f(x) = x/4;
Graph:
x f(x)
1 0.25
2 0.5
3 0.75
4 1
b. c = 1/30 so that f(x) = (1/30)x;
Graph:
x f(x)
1 0.03333
2 0.06667
3 0.1
4 0.13333
5 0.16667
6 0.2
7 0.23333
8 0.26667
9 0.3
10 0.33333
c. c = 1 so that f(x) = (1/4)x;
Graph:
x f(x)
1 0.25
2 0.125
3 0.0625
4 0.03125
d. c = 1/8 so that f(x) = (1/8)(x + 1)²;
Graph:
x f(x)
0 0.125
1 0.25
2 0.375
3 0.5
e. c = n so that f(x) = x/n;
Graph:
x f(x)
1 1/n
2 2/n
3 3/n
... ...
n 1
f. c = 1 so that f(x) = 1/(x + 1) − 1/(x + 2);
Graph:
x f(x)
0 1
1 0
2 −0.5
3 −0.333
4 −0.25
5 −0.2
... ...
For each of the functions, the constant c was determined so that the function would satisfy the conditions of being a pmf for a random variable X, and then a line graph was plotted for each pmf.
Learn more about graph here
https://brainly.com/question/17267403
#SPJ4
7. Write the decimal number 53.71 as a reduced fraction of two integers.
What is the larger and smaller solution.
The value of the equation is x = 4 and x = -5 ± √10i
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
( x - 4 ) / ( x + 5 ) + 9 / ( x² + 11x + 30 ) = 1/( x + 6 )
On simplifying the equation , we get
( x - 4 ) / ( x + 5 ) + 9 / ( x + 5 ) ( x + 6 ) = 1/( x + 6 )
Multiply the equation with the LCM , we get
( x - 4 ) ( x + 5 ) ( x + 6 ) + 9 ( x - 5 ) = ( x - 5 ) ( x + 5 )
x³ + 7x² - 14x - 120 + 9x - 45 = x² - 25
Subtracting x² on both sides of the equation , we get
x³+ 6x² - 5x - 165 = -25
Adding 25 on both sides of the equation , we get
x³+ 6x² - 5x - 140 = 0
Hence , the solution to the equation is x = 4 , -5 ± √10i
So , the larger solution is x = 4
And , the smaller solution is x = -5 ± √10i
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
if x and x are such numbers that x>0 and z<0 then which of the following is always correct
The statement that is always correct regarding the multiplication of x and z is given as follows:
The multiplication of x and z is always negative.
What are the multiplication signal rules?The multiplication signal rules is defined by the terms two by two, and the rule is given as follows:
Equal signs: positive product.Different signs: negative product.For this problem, we have that x and z have different signs, hence the product is going to be always negative.
More can be learned about the multiplication rules at https://brainly.com/question/847241
#SPJ1