Answer:
x = -0.8
Step-by-step explanation:
2.35+0.25x = 1.75+0.4
To find x, we must first isolate the value.
This is done by subtracting any values on the same side as the x.
Thus, we subtract 2.35 from both sides.
We are now left with the following:
0.25x=1.75+0.4-2.35
Now you should simplify the right side by finding the sum, which is -0.2, so:
0.25x=-0.2
Finally, solve by dividing each side by 0.25.
x = -0.8
Answer:
[tex]x = -\dfrac{4}{5} \ \ \textrm{or} \ \ x = -0.8[/tex]
Step-by-step explanation:
First, multiply both sides by 100 to make the numbers nicer to work with.
[tex](100)(2.35 + 0.25x) = (1.75 + 0.40)(100)[/tex]
[tex]235+25x=175+40[/tex]
Next, isolate x by moving all the constant terms to one side and then dividing by x's coefficient.
[tex]25x=175+40-235[/tex]
[tex]25x = -20\\\overline{\, \, 25 \, \,} \: \, \, \, \, \, \, \, \overline{ \,\, 25 \, \,}[/tex]
[tex]x = -\dfrac{20}{25}[/tex]
[tex]x = -\dfrac{4}{5}[/tex]
So, the value of x is -4/5 or 0.8.
an unbiased coin is tossed four times. what is the probability that coin lands heads up at least once? (round your answer to three decimal places.)
The probability of getting at least one head is 15/16.
What is probability?
The ratio of positive outcomes to all possible outcomes of an event is known as the probability.
Formula for probability = favourable outcomes/ total outcomes
Main body:
if 4 coins are tossed , total no. of outcomes = 2⁴ = 16
In a toss there are 2 outcomes T or H
so, Probability of getting Head = 1/2
The probability of getting at least 1 head = 1- probability of getting no heads
⇒1 - Probability of getting tail in 4 tosses
⇒ 1 - (1/2)⁴
⇒ 1 - 1/16
⇒ 15/16
So the probability of getting at least one head is 15/16.
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12▸ A road has a gradient of 1/15 for 90 m. Then there is a horizontal section 130 m long. The final section has a gradient of 1/25 for 200 m. a Find the total height gained from start to finish. b What is the average gradient from start to finish?
The total height gained from start to finish is 58m and the average gradient from start to finish is 29/210
What is an average gradient?
The gradient of a straight line drawn between two points is the average gradient between the two points.
Here, we have
A road has a gradient of 1/5 for 90 m.
Horizontal section 130 m long
The final section has a gradient of 1/5 for 200 m.
First, we will find the total height gained from start to finish
Total height from start to finish = 90 ×1/5 +200 × 1/5
= 18 + 40
Total height from start to finish =58 m
The average gradient from start to finish = 58/(90 + 130 +200)
= 58/420
= 29/210
Hence the total height gained from start to finish is 58m and the average gradient from start to finish is 29/210
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PLS HELP WITH THIS MATH
When we multiply the given inequality that is [tex](\frac{x^{2} - 25}{2x^{2} +10x +12})(\frac{x+6-x^{2} }{x^{2} +2x-15})[/tex], then we get the required equation as [tex](\frac{-x+5}{2x+6}) ; x[/tex] ≠ [tex]-3,3,-2,-5[/tex]
What is multiplication of inequalities ?If you multiply one side of an inequality by a number, you can multiply the other side of the inequality by the same number .
What is the condition of inequality ?The denominator should not be 0 that is the value of x .
Given: [tex](\frac{x^{2} - 25}{2x^{2} +10x +12})(\frac{x+6-x^{2} }{x^{2} +2x-15})[/tex]
On solving ,we get
[tex]=(\frac{(x+5)(x-5)}{2(x+2)(x+3)}) (\frac{(-1)(x-3)(x+2)}{(x-3)(x+5)})[/tex]
Since denominator cannot be equal to zero.
Therefore x ≠ -2, x ≠ -3
and x ≠ 3, x ≠ -5
So ,x ≠ -2,-3,3,-5
It is the condition for x .
On cancelling common terms ,we get
[tex]=(\frac{(-1)(x-5)}{(2)(x+3)})[/tex]
[tex]=(\frac{-x+5}{2x+6})[/tex]
This is the required equation obtained .
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(03.02 MC)
Elevator 1 in a hotel moved from ground position to a final position of +18 feet. Elevator 2 in the same building moved from ground to a final position of −20 feet. Which statement best describes the final positions of these two elevators?
Group of answer choices
A.) Elevator 1 is 18 feet below ground level, and Elevator 2 is 20 feet above ground level.
B.) Elevator 1 is 18 feet above ground level, and Elevator 2 is 20 feet below ground level.
C.) Elevator 1 is 18 feet below ground level, and Elevator 2 is 20 feet above the position of Elevator 1.
D.) Elevator 1 is 18 feet above ground level, and Elevator 2 is 20 feet below the position of Elevator 1.
Elevator 1 is 18 feet above ground level, and Elevator 2 is 20 feet below ground level.
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,
Elevator 1 in a hotel moved from ground position to a final position of +18 feet.
+18 means the elevator is 18 feet above the ground floor.
Elevator 2 in the same building moved from the ground to a final position of −20 feet.
-20 feet means the elevator is 20 below the ground floor.
Thus,
Elevator 1 is 18 feet above ground level, and Elevator 2 is 20 feet below ground level.
Option B is the correct answer.
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The figure to the right is comprised of a rectangle and two half circles. The rectangle is 100 ft wide and 10 ft long. Find the total area of the figure. Show your work and/or explain your reasoning.
A-1,000ft^2
B-1,314ft^2
C-120ft^2
D-1,078.5ft^2
Pls help
Answer:
D 1,078.5 ft^2
Step-by-step explanation:
You want the area of a figure composed of a rectangle 100 ft long and 10 ft wide with semicircles of diameter 10 ft at each end.
Rectangle AreaThe area of the rectangle is ...
A = LW
A = (100 ft)(10 ft) = 1000 ft²
Circle AreaThe two half-circles have the area of a whole circle with radius 5 ft.
A = πr²
A = π(5 ft)² = 25π ft² ≈ 78.5 ft²
Total AreaThe area of the figure is the sum of the areas of its parts:
total area = rectangle area + circle area
total area = 1000 ft² +78.5 ft² = 1078.5 ft²
The total area of the figure is about 1078.5 ft².
Work out the equation of the straight line that passes through (2, 3) and
(5, 18).
Give your answer in the form y = mx + c, where m and c are integers or
fractions in their simplest forms.
Answer:
Y=5X-7
Step-by-step explanation:
(2,3)
Y-Yo=m(X-Xo)
Y-3=m(X-2)
Y-3=mX-2m
Y=mX-2m+3
(5,18)
18=m(5)-2m+3
18=5m-2m+3
18=3m+3
18-3=3m
15=3m
15/3=m
5=m
Y=5X-2(5)+3
Y=5X-10+3
Y=5X-7
Write the equation of the line that passes through (7,- 4) and
(-1, -2) in slope-intercept form.
Calculate height of lighthouse pls :) thx
The height of lighthouse is 72.54
Given,
In the question:
To see the figure:
To find the height of lighthouse.
Now, According to the question:
In Triangle ABD
tan 20° = [tex]\frac{h}{20 + x}[/tex]
0.36 = [tex]\frac{h}{20 + x}[/tex]
=> (20 + x)0.36 = h
=> 0.72 + 0.36x = h
=> x = [tex]\frac{h - 72}{0.36}[/tex] .....(1)
In Triangle ABC
tan 34° = h/x
=> 0.67 = [tex]\frac{h}{\frac{h-72}{0.36} }[/tex]
=> 0.67 = 0.36/h - 72
=> 0.67 (h - 72) = 0.36
=> h - 72 = 0.54
=> h = 0.54 + 72
=> h = 72.54
Hence, The height of lighthouse is 72.54
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Question 1 (1 point) Which pair of equations represents lines that are perpendicular Y=2x+8 y = 2x + 2 y = 1/2x +4 y = -2x-3 y 1/2x + 3 y = 2x-4
Only y = - 2x - 3...(iv) and y = (1/2)x...(v) are perpendicular to each other as the negative reciprocal of - 2 is 1/2.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know lines that are perpendicular to each other have a slope that is negative reciprocal of each other.
The given lines are,
y = 2x + 8...(i)
y = 2x...(ii)
2y = (1/2)x + 4.
y = (1/4)x + 2...(iii)
y = - 2x - 3...(iv).
y = (1/2)x...(v)
3y = 2x - 4.
y = (2/3)x - 4/3...(vi)
So, only y = - 2x - 3...(iv) and y = (1/2)x...(v) are perpendicular to each other as the negative reciprocal of - 2 is 1/2.
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How do you find the average of 1 to 100?.
The first 100 natural numbers are 1,2,3,...,100 is 50.5.
An average is a single number chosen to represent a group of numbers; it is typically the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.
We know that the sum of the first n natural numbers is = 2n(n+1)
Therefore, the sum of the first 100 natural numbers is = 2×100(101)
=200(101)=20200
Hence, the sum of the first 100 natural numbers is = 20200 = 101
200
Hence, the average of the first 100 natural numbers is = 101 = 50.5
2
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how do you do that 52 + 19 = 71
Answer:
1
52
+ 19
____
71
Step-by-step explanation:
add 2+9 and get 11
carry the one
add 1+1+5 and get 7
71
a company advertises that its training program raises sat scores by an average of at least 30 points. a random sample of test-takers who had completed the training showed a mean increase smaller than 30 points. write the hypotheses for a left-tailed test of the mean
Type - I error states that the training program actually raised the score but statistically, it is not.
Type-II error states that the training program does not actually raise the score but statistically, it raised the scores.
Given statement is
"A random sample of test-takers who had completed the training showed a mean increase smaller than 30 points."
Hypothesis is,
Null hypothesis H0 :μ ≥ 30 (claim)
Alternate hypothesis H1 :μ < 30 (actual result)
in the null hypothesis, we have to consider the claim and the other in the alternate hypothesis.
In the given context of the problem, the Type-1 error will be stated below
" If in reality, the training program raises the SAT score by more than or equal to 30 points and statistically the claim is rejected".
The training program actually raised the score but statistically, it is not.
Type-II error
" If in reality, the training program does not raise the SAT score by more than or equal to 30 points and statistically the claim is failed to reject".
The training program does not actually raise the score but statistically, it raised the scores.
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HI PLS HELP ME ON MY MATH HOMEWORK I WILL ALSO GIVE BRAINLIEST
Considering the parallel and triangle sum properties and the isosceles triangle properties the only correct part option is 2
How to interpret the figuresOption 1
The angle 52 degrees is base angle of isosceles triangle therefore say angle at the third angle is x such that
x + 52 + 52 = 180 (triangle sum property)
x + 104 = 180
x = 76
The figure shows that the base angle of the triangle at the base is equal to 76 too
32 + 2x = 180 (triangle sum property for isosceles triangle)
x = 74
The two angles 74 and 76 are not equal - wrong option
Option 2
x + 2 * 76 = 180 (triangle sum property for isosceles triangle)
x = 28
The figure shows that the base angle of the triangle at the base is equal to 28
124 + 2x = 180 (triangle sum property for isosceles triangle)
x = 28
The two angles 28 and 28 are equal hence a right option
Option 3
wood you believe it, I past plain geometry - wrong
would you believe it, I passed plain geometry - correct
Option 4
The triangle in the parallelogram the isosceles triangle with base angle 27
The alternate interior angle is showing same base angle as 29
and the two angles 27 and 29 are not equal
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A recipe for a single sheet of brownies asks for ¼ cup of flour. You want to make 5 sheets of brownies. How much flour do you need?
Answer:
1 1/4 cup of flour
Step-by-step explanation:
1/4 × 5 = 1 1/4
Which if the following represents the location of any unit rate, m, as graphed on a coordinate plane?
(1) (1, m) (3) (0, m)
(2) (m, 1) (4) (m, 0)
The answer choice which represents the location of any unit rate, m as graphed on a coordinating plane is; Choice 1; (1, m).
Unit rate on a coordinate planeIt follows from the task content that the answer choice which represents the location of any unit rate, m on a coordinate plane.
Hence, since the slope is defined as the rate of change on a graph such that slope = ∆y/∆x.
In this case, when the change in y with respect to x is to be equal to m.
Therefore, the location as required is the point defined by; (1, m).
Such that; Unit rate = (m - 0)/(1 - 0)
Ultimately, the required location of the unit rate is; Choice 1; (1, m).
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Lupita ride a taxi that charge a flate rate of $6. 75 plu $3. 20 per mile. If the taxi charge lupita $40. 03 in total for her trip , how many mile i her ride ?
Based on the charged amount, Lupita drove 8.76 miles.
Let us assume the number of miles rode bh Lupita be x. Forming the equation now -
Total charge = flat rate + cost per mile × number of miles
Keep the values in above mentioned equation to find the value of x
40.03 = 6.75 + 3.20×x
Rewriting the equation with respect to x
3.20x = 40.03 - 6.75
3.20x = 33.28
Shifting 3.20 to Right Hand Side of the equation
x = 33.28 ÷ 3.20
Performing division on Right Hand Side of the equation
x = 8.76 miles
Thus, Lupita drove 8.76 miles.
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A regular polygon is shown, with the measure of one of its angles labeled 7x − 21. 9 sided regular polygon with one angle labeled 7 times x minus 21 Determine the value of x. x = 17 x = 23 x = 29 x = 140
The correct value of x = 23.
Each interior angle of an n-sided regular polygon is given by 180 (n-2)/n degrees.
Given that:
n = 9
Therefore, each interior angle＝180 x (9-2)/9 degrees
Each interior angle = 180 x 7/9
Each interior angle = 140°
Each internal angle of a regular polygon having 9 sides is 140°.
Also, given that:
A 9-sided regular polygon with one angle equals 7x-21.
For the polygon to be a 9-sided regular polygon, the angles must equal 140°.
Checking the value of x from the given option which one satisfies the value of interior angle = 140°.
Option 1, x= 17
=> 7 x 17 - 21 = 98° which is wrong.
Option 2, x= 23
=> 7 x 23 - 21 = 161-21 = 140° which is correct.
Option 3, x= 29
=> 7 x 29 - 21 = 203-21 = 182° which is wrong.
Option 4, x= 140
=> 7 x 140 - 21 = 980- 21 = 959° which is wrong.
Only, the value of x = 23 satisfies the value of a 9-sided regular polygon with one angle equal to 7x-21.
Hence, the correct value of x = 23
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Answer:
The correct value of x = 23.
Step-by-step explanation:
Please help me out with this
Answer:
6\sqrt3
Step-by-step explanation:
Since 30-60-90 tri, small side is 6.
This means x=[tex]6\sqrt3[/tex]
Answer:
[tex]x = 6\sqrt{3}[/tex]
Step-by-step explanation:
Utilize the trigonometric ratio cosine.
[tex]\cos(30\textdegree ) = \dfrac{x}{12}[/tex]
Solve for x by multiplying both sides by 12.
[tex]12\cos(30\textdegree ) = x[/tex]
[tex]12\left(\dfrac{\sqrt{3}}{2} \right) = x[/tex]
[tex]x = 6\sqrt{3}[/tex]
A company has a target profit of $204,000. The company's fixed costs are $305,000. The contribution margin per unit is $40. What is the break-even point in unit sales?
7,625 units
breakeven point= $305,000/$40=7,625
The break-even point in unit sales of the company is $7,625.
Define the term break-even point?The break-even threshold is reached when overall costs and total revenues are equal, leaving your small firm with no net benefit or loss. In other words, you've achieved the point in production where the revenue from a product equals the cost of manufacture.According to the question,
A corporation aims to make $204,000 in profit.The corporation has $305,000 in fixed expenses.The contribution margin is $40 for each unit.Thus,
Break-even point = fixed costs/margin per unit
Break-even point = $305,000/$40
Break-even point = $7,625
Thus, the break-even point in unit sales of the company is $7,625.
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Solve for the side or angle in the right triangles below. Show all of your work....
1)
X
12
18°
2)
25
10
The side and angle is in the right angle triangle respectively x = 3, 68°.
What is a right angle triangle?
A right triangle, also known as a right-angled triangle, is a triangle with one angle that is a right angle (i.e., a 90-degree angle) and two perpendicular sides.
We have,
[tex]1) Opposite = x, \ Adjustment = 12, \ \theta = 18.\\\\2) Opposite = 25, \ Adjustment = 10, \ \theta = ?.[/tex]
How to determine the angle in a right angled triangle,
[tex]Sin (\theta ) = \frac{Opposite}{Hypotenuse}[/tex][tex]Tan (\theta ) = \frac{opposite}{adjacent}[/tex]
[tex]cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]1) \ Opposite = x, Adjustment = 12, \ \theta = 18.[/tex]
[tex]cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]Hypotenuse = \frac{Adjacent}{cos(\theta)}[/tex]
[tex]Hypotenuse = \frac{Adjacent}{cos(18)}[/tex]
[tex]= 12.61755[/tex]
[tex]Opposite = \sqrt{Hypotenuse^{2} - Adjacent^{2} }[/tex]
[tex]= \sqrt{12.6175466908592 - 122}[/tex]
[tex]= \sqrt{15.202484496012}[/tex]
∴ [tex]Opposite(x) = 3.89904[/tex]
[tex]2) \ Opposite = 25, \ Adjustment = 10, \ \theta = ?.[/tex]
[tex]Hypotenuse = \sqrt{{Opposite^{2} - Adjacent^{2} }[/tex]
[tex]= \sqrt{25^{2} + 10^{2} }[/tex]
[tex]= \sqrt{725} \\\\= \ 26.92582 \ = \ 5\sqrt{29}[/tex]
[tex]\theta =\ sin^{-1} {\frac{Opposite }{Hypotenuse} }[/tex]
[tex]\theta = \ sin^{-1} (\frac{25}{26.92} )[/tex]
[tex]\theta = \ sin^{-1} (\frac{25}{26.92} )[/tex]
[tex]= sin^{-1} (0.92847669088526)[/tex]
[tex]\theta = \ 68[/tex]°
Hence, The side and angle is in the right angle triangle respectively x = 3, 68°.
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Which symbol correctly compares these two fractions?
6/10 ? 5/7
A. <
B. =
C. >
Answer:
A. <
Step-by-step explanation:
Hope this helps! ^^
Answer:
>
Step-by-step explanation:
2/5 is greater than 7/10. Therefore, the best symbol to compare the two would be the greater than symbol, >.
ignoring twins and other multiple births, assume that babies born at a hospital are independent random events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. what is the probability that at least one of the next three babies is a boy?
The probability that at least one of the next three babies is a boy is 0.875.
What is probability ?Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.
CalculationProbability of the complement of event B:
The probability of the complement of event B is computed as follows:
P(B* )=1-P(B) P(B)=14(1-(0.5x0.5)) = 0.25
The probability of the complement of event B is B) 0.25.
Probability that at least one of the next three babies is a boy:
The probability that at least one of the next three babies is a boy is computed as follows:
at least one of the next three babies is a boy =1-(0.5x0.5x0.5) =1-0.125 = 0.875
The probability that at least one of the next three babies is a boy is D) 0.875.
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A photocopier take 8 econd to make 20 copie. How long will it take to make 45 copie?
Given that a photocopier takes 8s to make 20 copies and we need to find out how long would it take to make 45 copies .
This can be solved using Unitary Method as ,
To make 20 copies it takes 8 s.
To make 1 copy it would take 8/20 s
Hence to make 45 copies it would take 8/20*45 = 18s
And we are done!
Answer:
45 copies = 18 seconds
Step-by-step explanation:
Time taken to make 1 copy,
→ Total time ÷ Total copies
→ 8 ÷ 20
→ 8/20 seconds
Then the time taken for 45 copies,
→ 45 × (8/20)
→ (45 × 8)/20
→ 360/20
→ 18 seconds
Hence, time taken is 18 seconds.
The sum of 8 and a certain number is equal
to the product of the number and 3. Find
the number.
Answer:
4
Step-by-step explanation:
1.) Create an equation. If we let the number be x, we get x+8=3x
2.) Solve. If you move x to the other side, we get 2x=8. Finally, by dividing by 2 on each side, we get x=4. Therefore, the number is 4.
Answer:
4
Step-by-step explanation:
create an equation thus 8+x =3x
8+X=3x
collect like terms
8=3x-x
8=2x
divide both sides by 2
8/2=2x/2
X=4
Simplify x raised to the negative second power over y raised to the fourth power.
y raised to the fourth power over x raised to the negative second power
y raised to the fourth power over x raised to the second power
1 over the quantity x raised to the second power times y raised to the fourth power end quantity
−x2y4
Answer:
Step-by-step explanation:
(x 2 y) 4 = x2*4 y 1*4 = x 8 y4
An exponent raised to another exponent means to multiply the exponents. If a number does not have a visible exponent, then it is an implied 1.
The required simplified form of the expression is 1 / (x² · y⁴) which is the correct answer would be an option (D).
How to use laws of exponents?When multiplying similar bases, keep the base and add the exponents the same. When comparing one power to another, keep the base constant and multiply the exponents. Keep the base constant when dividing like bases and subtract the denominator exponent from the numerator exponent.
Simplify x raised to the negative second power over y raised to the fourth power.
The expression is given in the question below as:
x⁻² / y⁴
The expression can be simplified as follows:
⇒ x⁻² / y⁴
⇒ (1 / x²) / (y⁴)
⇒ 1 / (x²) · y⁴)
⇒ 1 / (x² · y⁴)
Therefore, the simplified form of the expression is 1 / (x² · y⁴).
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there is a total of 85 tiles work out the number of blue tiles
The number of blue tiles is 68.
Given:
Red tiles = 1/5 of the total
Total tiles = 85
Red tiles = 1/5*85
= 17.
Number of blue tiles = total tiles - red tiles
= 85 - 17
= 68.
Therefore the number of blue tiles is 68.
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please help me solve this simultaneous eqn
x+y=7
2x² + y² = 35-3xy
Answer:
x = -2, y = 9
Step-by-step explanation:
x + y = 7 --1
2x² + y² = 35 - 3xy --2
For 1, make y the subject.
y = 7 - x
Substitute y = 7 - x into 2.
2x² + (7 - x)² = 35 - 3x(7 - x)
Simplify and solve for x.
2x² + (49 - 14x + x²) = 35 - 21x + 3x²
3x² - 14x + 49 = 3x² - 21x + 35
7x = -14
x = -2
Substitute x = -2 into y = 7 - x.
y = 7 - (-2)
= 9
Thus, x = -2, y = 9
Gaton paint a pole uing three different colour a hown. What i the ratio for the length of grey to red to blue? Give your anwer in it implet form uing whole number only. Grey 0. 8 m Red 1. 8 m Blue 0. 6 m Not to cale
The ratio for the length of grey to red to bule is 4:9:3.
What is ratio?Ratio is the relation between two numbers which shows how much bigger one quantity than another. Ratio show how many times one contain show the other one.
According to the question
The given data are -
Grey = 0.8m
Red = 1.8 m
Bule = 0.6 m
By solving these we can get -
=0.8:1.8:0.6
=0.8×10:1.8×10: 0.6×10
=8:18:6
By simplifying it we can get
4:9:3.
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Joey has 42 marbles. He has 7 times as many marbles as Sam has. How many marbles does Sam have? *
Answer:
Sam has 6 marbles
Step-by-step explanation:
42 ÷ 7 = 6
7 times means that whatever Joey has it is sams × 7. so to find answer we the do reserve.
Write the answers in lowest terms leave improper fractions when applicable.Ron not convert to mixed numbers
