Janet has to pay off $65 to reduce her balance to no more than $60.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Janet has a balance of 125 on a credit card on her next statement she wants to reduce her balance to no more than 60.
The amount to be paid will be calculated as,
Amount = 125 - 60
Amount = $65
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The equation of line AB is (y-3)=5(x-4) what is the slope of a line perpendicular to line AB
Evaluate (4/9)^1/2
help would be great
To evaluate (4/9)^1/2, you find the square root of 4, which is 2, and the square root of 9, which is 3, hence the result is 2/3.
The student has asked to evaluate the expression (4/9)^1/2. To do this, you take the square root of both the numerator and the denominator separately. The square root of 4 is 2 and the square root of 9 is 3, therefore, the evaluation of the expression (4/9)^1/2 is equivalent to 2/3.
Given that the standard error of the sample proportion is 0.0195 and the point estimate follows a nearly normal distribution, calculate the test statistic (the z-statistic).
Nearsighted. It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted.
(a) Construct hypotheses appropriate for the following question: do these data provide evidence that the 8% value is inaccurate?
(b) What proportion of children in this sample are nearsighted?
(c) Given that the standard error of the sample proportion is 0.0195 and the point estimate follows a nearly normal distribution, calculate the test statistic (the Z-statistic).
(d) What is the p-value for this hypothesis test?
(e) What is the conclusion of the hypothesis test?
Part A:Solve for x. x−4.76=−7
Introduction to addition or subraction of fractions with different denominator 2/3+1/4
Would someone please help me out with Geometry?? I tried yesterday with other questions and got no help.
Thank you so much!!
Jose is painting a backdrop for the school play. The rectangular backdrop is 60 inches by 45 inches. If his container of paint can cover 25 square feet, does he have enough paint to paint the backdrop?
The area of a rectangular backdrop is 18.75 square feet and container has enough paint.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Given that, the rectangular backdrop is 60 inches by 45 inches.
We know that, 1 feet =12 inches
So, 60 inches = 60/12 = 5 inches
45 inches = 45/12 = 3.75 inches
Here, Area = 5×3.75
= 18.75 square feet
If his container of paint can cover 25 square feet.
So, Jose has enough paint.
Therefore, the area of a rectangular backdrop is 18.75 square feet and container has enough paint.
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A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 568 feet of fencing is used. find the dimensions of the playground that maximize the total enclosed area. remember to reduce any fractions and simplify your answers as much as possible.
Write 4.7 as a mixed number with a fraction in simplest form.
A) 4/7
B) 7/10
C) 4 1/7
D) 4 7/10
Answer:
D) 4 7/10
Step-by-step explanation:
Any fraction may be written as a mixed number. This type of number is formed by one or more whole parts plus a fractional part.
4.7 = 4 + 0.7
4 + 7/10
4 7/10
Following this same reasoning we can turn a mixed number into improper fraction and improper fraction into mixed number.
5k+(−2k)−(−1) what is the answer please give it to me
there are 18 rows of seats in the auditorium there are 24 seats in each row how many seats are in the auditorium in all
In ΔABC shown below, ∠BAC is congruent to ∠BCA:
Given: Base ∠BAC and ∠ACB are congruent.
Prove: ΔABC is an isosceles triangle.
When completed (fill in the blanks), the following paragraph proves that Line segment AB is congruent to Line segment BC making ΔABC an isosceles triangle.
Construct a perpendicular bisector from point B to Line segment AC.
Label the point of intersection between this perpendicular bisector and Line segment AC as point D:
m∠BDA and m∠BDC is 90° by the definition of a perpendicular bisector.
∠BDA is congruent to ∠BDC by the definition of congruent angles.
Line segment AD is congruent to Line segment DC by _______1________.
ΔBAD is congruent to ΔBCD by the _______2________.
Line segment AB is congruent to Line segment BC because corresponding parts of congruent triangles are congruent (CPCTC).
Consequently, ΔABC is isosceles by definition of an isosceles triangle.
Fill in the blanks 1 & 2.
A. 1. Angle-Side-Angle (ASA) Postulate
2. corresponding parts of congruent triangles are congruent (CPCTC)
B. 1. corresponding parts of congruent triangles are congruent (CPCTC)
2.Angle-Side-Angle (ASA) Postulate
C. 1. the definition of a perpendicular bisector
2. Angle-Side-Angle (ASA) Postulate
D. 1. corresponding parts of congruent triangles are congruent (CPCTC)
2. the definition of a perpendicular bisector
Decide which of the two points lies on the graph of the line
X= -3
A. 2,-3
B. -3,2
The measurement of the complement of an angle exceeds the measure of the angle by 25%. Find the measurement of the angle and its complement.
The angle measures 40 degrees, and its complement, which is 25% larger than the angle, measures 50 degrees. This is solved using elementary algebra by setting up an equation with the angle as 'x' and its complement as '90-x', and then simplifying the equation to solve for 'x'.
Explanation:The question involves finding the measure of an angle and its complement when given that the complement exceeds the measurement of the angle by 25%. To solve this, let's use algebra. Let the measure of the angle be x degrees.
Since the complement of an angle adds up to 90 degrees with the angle itself, the complement can be represented as 90 - x degrees. According to the problem, the complement is 25% more than the angle, so we can write the equation:
90 - x = x + 0.25x
Simplifying, we get:
90 - x = 1.25x
90 = 2.25x
Dividing both sides by 2.25 gives us the measure of the angle x:
x = 40 degrees
Since the complement is 90 - x, we find:
Complement = 90 - 40 = 50 degrees
Therefore, the angle measures 40 degrees, and its complement measures 50 degrees.
A water tank can hold 234 cubic meters of water. How many gallons can the water tank hold?
A. 6,176 gallons
B. 61,776 gallons
C. .886 gallons
D. 23,400 gallons
a fire departments longest ladder is 110 feet long, and the safety regultion states that they can use it for resue up to 100 feet off the ground. what is the maximum safe angle of elevation for the rescue ladder?
To find the maximum safe angle of elevation for a 110-foot ladder used at a height of 100 feet, we use the tangent inverse function with the ladder's maximum safe height as the opposite side and the ladder's hypothetical base length as the adjacent side. The angle of elevation is calculated using θ = tan⁻¹(100/adjacent). The specific calculation of the adjacent side isn't needed as the angle of elevation will be the same regardless of the actual length of the ladder along the ground.
Explanation:The question is asking to find the maximum safe angle of elevation at which a 110-foot fire department ladder can be used, given that it can be safely used for rescues up to 100 feet off the ground. This is a trigonometry problem that involves the use of right-angled triangles.
To solve this problem, we will use the trigonometric function tangent (tan), which relates the angle of elevation θ to the opposite side of the triangle (the height of the building) and the adjacent side (the length of the ladder along the ground). The formula is θ=tan⁻¹(opposite/adjacent).
In this case, the opposite side is the maximum safe height of 100 feet, and the adjacent side would be the length of the ladder laid on the ground when the ladder reaches 100 feet high. We can find the length of the adjacent side using the Pythagorean theorem. However, we do not need to calculate it, as the angle of elevation does not depend on the horizontal distance but only on the ratio of the opposite side to the adjacent side.
The calculation would be: θ = tan⁻¹(100/adjacent).
Since the ladder length is greater than the height it needs to reach, the ladder base (adjacent) will be inside the triangle formed by the ladder and the building. The maximum safe angle of elevation θ can be calculated using the inverse tangent function of the height over the hypothetical base length, which is less than 110 feet.
Focus tests suggest that costumers love the new gPhone X1, but they think the 5.82-inch long screen is too long. The engineers come back with a design they called the gPhone X2 with a screen that is 5/8 inch shorter than the X1. Will the new X2 be shorter that its main competitor, the 5 1/5-inch rover 6?
What is 7.984 ÷ 1.99
Answer:
4.012 to 3 decimal places
Step-by-step explanation:
The division of decimal numbers can be done easily by multiplying the numerator and denominator with a number whose power of 10 completely removes the decimal.
For 7.984 ÷ 1.99
= (7.984 × 10^3) ÷ (1.99 × 10^3)
= 7984/1990
= 4.012060302
≈ 4.012 to 3 decimal places
Identify the transformation that does NOT map the figure onto itself.
A) Reflect across the line y = 1
B) Reflect across the line x = 1
C) Rotate 180° about the point (1, 1)
D) Rotate 180° about the origin (0, 0)
Answer:
D.Rotate 180 about the origin (0,0)
Step-by-step explanation:
Suppose a triangle has sides a, b, and c, and let theta be the angle opposite the side of length a. If cos theta > 0 what must be true?
A. a2 + b2 > c2
B. a2 + b2 = c2
C. b2 + c2 < a2
D. b2 + c2 > a2
When cosθ >0 then , b² + c² > a².
What is triangle?
" Triangle is a 2 dimensional shape which is having three sides and three vertices. Sum of all the interior angles of a triangle is 180°."
Formula used
As per Cosine Rule
For a given ΔABC,
cosθ = [tex]\frac{b^{2} + c^{2} - a^{2} }{2bc}[/tex]
According to the question,
cosθ >0
⇒ [tex]\frac{b^{2} + c^{2}-a^{2} }{2bc}[/tex] >0
⇒ b² + c² >a²
Hence, we conclude that Option D is correct.
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Please help with math question!
PLZ HELP!! I WILL VOTE BRAINLIEST
What is the point slope form of the line with slope 25 that passes through the point (−4, −7) ?
y+7=25(x+4)
y−7=25(x−4)
y+4=25(x+7)
y−4=25(x−7)
Answer: [tex]y+7=25(x+4)[/tex]
Step-by-step explanation:
We know that the point slope form of a line that passing through (a,b) and has slope m is given by :-
[tex](y-b)=m(x-a)[/tex]
Given : Slope: m = 25 ; Point : (a,b) =(−4, −7)
Then, the point slope form of the line with slope 25 that passes through the point (−4, −7) will be :-
[tex](y-(-7))=25(x-(-4))\\\\\Rightarrow\ y+7=25(x+4)[/tex]
Describe how to graph an inequality
Graphing an inequality is a great way to visualize a range of possible solutions and steps for graphing the inequality are shown below.
We have to give that,
Graph of inequality.
Here's a step-by-step guide to help graph an inequality:
Step 1:
Understand the inequality. Start by reading and understanding the given inequality. Is it greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤) inequality? This will determine the type of graph you will create.
Step 2:
Convert the inequality into slope-intercept form if possible. Rewrite the inequality in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Step 3:
Plot the y-intercept. Identify the y-intercept from the equation obtained in Step 2, and mark it on the graph. This is the point where the line crosses the y-axis.
Step 4:
Determine the slope. If the inequality is in slope-intercept form, the coefficient of x will be your slope. If not, rearrange the inequality to isolate y and find the coefficient of x to determine the slope.
Step 5:
Plot additional points. Use the slope to find one or two more points on the line. To do this, start from the y-intercept and move up or down based on the slope (rise over run). Connect these points to form a line.
Step 6: Determine the shading. Determine whether the inequality represents a region above or below the line. If the inequality is greater than or greater than or equal to, shade the region above the line. If the inequality is less than or less than or equal to, shade the region below the line. You can use dots or arrows to indicate whether the line is included or not.
Step 7: Finalize the graph. Extend the line beyond the plotted points, making sure it remains parallel. Then, label the graph and include any necessary units or context.
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Walter's savings account has a balance of $273. After 5 years, what will the amount of interest be at 5% compounded quarterly? a. $6.83 c. $77.00 b. $68.00 d. $82.00
Answer:
c
Step-by-step explanation:
Kyle is converting 13°F to °C. His work is shown. Is Kyle's answer correct? If not, find his mistake and determine the correct answer to the nearest degree. Given: 5 9 (°F − 32) Step 1: 5 9 (13°F − 32) Step 2: 5 9 (45) Step 3: 25° C
Given:
The temperature is given in Fahrenheit (13 degree F).
To Find:
The correct temperature in Celsius.
Answer:
The temperature in Celsius is approximately -11 degree C.
Kyle has got an incorrect answer because instead of subtracting 32 form the temperature, he has added it.
Step-by-step explanation:
Any temperature can be changed from F to C by using the formula
[tex]C=(\frac{5}{9})(F-32)\\\\C=\frac{5(F-32)}{9}[/tex]
So, we will convert the given temperature in F to C by performing three simple steps.
Step 1 - We will subtract 32 from the Fahrenheit temperature.
Step 2 - Multiply this number by 5.
Step 3 - Divide the resulting number by 9.
So,
Step 1: 13-32 = -19
Step 2: -19*5 = -95
Step 3: -95/9 = -10.55 approx
Thus, the temperature in Celsius is approximately -11 degree C.
Kyle has got an incorrect answer because instead of subtracting 32 form the temperature, he has added it.
Kyle has got an incorrect answer because instead of subtracting 32 form the temperature, he has added it.
Given:
Kyle is converting 13°F to °C.
The formula used to convert F to C is
C= 5/9 (F- 32)
Now, Substitute F= 13 into the formulas as
C= 5/9 (13 - 32)
C = 5/9 (-19)
C= -95/ 9
C= -10.55
Thus, the temperature in Celsius is -11 degree C.
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What is the length of PR?
PR = QR
5n = 32 +n
subtract 1 n from each side
4n = 32
divide both sides by 4
n = 32/4 = 8
n=8
PR = 5n = 5*8 = 40
PR = 40
The measure of PR from the diagram given is 40
The given diagram is an isosceles triangle, For an isosceles triangle, two of sides and angles are equal. hence;
PR = QR
5n = 32 + n
Collect the like terms;
5n - n = 32
4n = 32
n = 32/4
n = 8
Get the measure of PR;
PR = 5n
PR = 5(8)
PR = 40
Hence the measure of PR from the diagram given is 40
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HELP QUICK!!!
Find negative square root of 36.
A. ±6
B. −6
C. 6
D. 18
which equation is equivalent to y-6=-12(x+4) a. y=-6x-48 b. y=6x-48 c. y=-12x-42 d. y=-12x-54
Answer:
C. is correct
Step-by-step explanation:
The equation equivalent to y - 6 = -12(x + 4) is c. y = -12x - 42.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now the given equation is,
y - 6 = -12(x + 4)
Expanding the bracket we get,
y - 6 = -12x - 48
Adding 6 both the side we get,
y - 6 + 6 = -12x - 48 + 6
Solving we get,
y = -12x - 42
which is equivalent to the given equation.
Thus, the equation equivalent to y - 6 = -12(x + 4) is c. y = -12x - 42.
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Find the volume of the triangular prism.
A. 120 yd3
B. 130 yd3
C. 240 yd3
D. 260 yd3
Cameron estimates that the math class will sell 200 calendars what will the total income be
Original equation c=2.50x+500