Answer:
Step-by-step explanation:
Well it is 3/5 of 7 we can convert that into 60% since multiplying the denominator and numerator by 2 equals to 6/10 or 60%. To find 10% of 7 move the decimal point back one is it is 0.7. Now multiply it by 6 and you get 4.2 = 3/5 of 7
What is the volume, in cubic m, of a cube with an edge length of 14m? (SERIOUS ANSWERS ONLY)
Answer: V = 2744 m3
Step-by-step explanation: I took the test and was correct
The answer of this question is above in the picture
A four-sided shape with the top side labeled as 10.2 cm. The height is labeled 5 cm. A portion of the base from the perpendicular to a vertex is labeled 4 cm. The portion of the base from the perpendicular to the right vertex is 6.2 cm.
What is the area of the figure?
25.5 cm2
45.5 cm2
51 cm2
56.1 cm2
The area of the figure is 51 cm², which is option C.
What is area?In mathematics, area refers to the measure of the size of a two-dimensional surface or shape. It is typically expressed in square units, such as square meters (m²) or square centimeters (cm²), and can be calculated for a variety of geometric shapes, including squares, rectangles, triangles, circles, and more complex shapes such as trapezoids or polygons.
To find the area of the figure, we need to identify the shape of the figure. From the given information, we know that the figure has a top side, a height, and a base. We are also told that the base is divided into two parts by a perpendicular, and one of the parts is labeled as 4 cm, while the other part from the perpendicular to the right vertex is 6.2 cm.
Based on this information, we can draw the figure as a trapezoid, where the top side is the shorter base, the height is the vertical distance between the two bases, and the longer base is the sum of the two parts of the base.
Using the given information, we can calculate the longer base:
longer base = 4 cm + 6.2 cm = 10.2 cm
Now we can use the formula for the area of a trapezoid to find the area of the figure:
A = (1/2)h(b₁ + b₂)
where h is the height, b₁ is the shorter base, and b₂ is the longer base.
Plugging in the given values, we get:
A = (1/2)(5 cm)(10.2 cm + 10.2 cm) = 51 cm²
Therefore, the area of the figure is 51 cm² , which is option C.
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Complete Question:
A four-sided figure has one side labeled 10.2 cm, a height of 5 cm, and a portion of the base from the perpendicular to a vertex labeled 4 cm. The portion of the base from the perpendicular to the right vertex is labeled 6.2 cm. What is the area of the figure?
I need this by today at 11:59 PM please help.
From given sample space, No. of toothpicks each student will get is 51.
What exactly is a sample space?
In mathematics, a sample space is the set of all possible outcomes of an experiment or a random phenomenon. It is denoted by the symbol "S" and is a fundamental concept used in calculating probabilities. For example, when flipping a coin, the sample space is {heads, tails}. When rolling a fair six-sided die, the sample space is {1, 2, 3, 4, 5, 6}. The sample space for a more complex event may involve multiple variables and outcomes.
Now,
Total Toothpicks = 918
Total students = 18
then
Toothpicks per student = 918/18=51
Hence,
No. of toothpicks each student will get is 51.
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A savings account starts with $312.50. After 9 years of continuous compounding at an interest rate, r, the account has $1250.
What is the interest rate percentage?
Round the answer to the nearest hundredth.
someone said it was 10.98% but i submitted that and it said it was wrong so i do not know
Okay, let's walk through this step-by-step:
The initial balance of the savings account: $312.50
The final balance after 9 years: $1250
Let's call the interest rate r.
We know the final balance is the initial balance times (1 + r)^9
(because of continuous compounding over 9 years)
So:
312.50 = (1 + r)^9
312.50 / (1 + r)^9 = 1250
Solving for r:
(312.50 / 1250)^(1/9) = 1 + r
0.2504 = 1 + r
0.7596 = r
Converting to a percentage:
0.7596 * 100% = 75.96%
Rounding to the nearest whole percent: 76%
So the interest rate is 76%.
Does this make sense? Let me know if you have any other questions!
if h(x) =x+2/x-2, then dy/dx= ?
Answer: To find the derivative of the function h(x), we can use the quotient rule, which states that if f(x) = u(x) / v(x), then f'(x) = [v(x)u'(x) - u(x)v'(x)] / [v(x)]^2.
Using this rule, we can find the derivative of h(x) as follows:
h(x) = (x + 2) / (x - 2)
h'(x) = [(x - 2)(1) - (x + 2)(1)] / (x - 2)^2 // apply the quotient rule and differentiate numerator and denominator
h'(x) = (-2 - 2x) / (x - 2)^2
Therefore, the derivative of h(x) is h'(x) = (-2 - 2x) / (x - 2)^2.
Step-by-step explanation:
Julian invested $990 in an account paying an interest rate of 6.2% compounded
continuously. Assuming no deposits or withdrawals are made, how much money, to
the nearest dollar, would be in the account after 12 years?
There would be $2,085 in the account after 12 years.
To solve this problem
The formula for calculating the amount of money in an account after a certain number of years with continuous compounding is:
A = Pe^(rt)
Where
A is the amount of money in the account after t yearsP is the principal (initial investment)e is the mathematical constant approximately equal to 2.71828 r is the annual interest rate (as a decimal) t is the time period in yearsIn this case, Julian invested $990 at an annual interest rate of 6.2% compounded continuously, which means r = 0.062. We want to find the amount of money in the account after 12 years, so t = 12. Using these values, we can plug into the formula and solve for A:
A = Pe^(rt)
A = $990 * e^(0.062*12)
A = $990 * e^(0.744)
A = $990 * 2.105
A = $2,084.95
Therefore, to the nearest dollar, there would be $2,085 in the account after 12 years.
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Answer:
Step-by-step explanation:
The correct answer is 2083
Polygon ABCD is drawn with vertices at A(1, 5), B(1, 0), C(−1, −1), D(−4, 2). Determine the image vertices of A′ if the preimage is rotated 270° counterclockwise.
A′(−1, −5)
A′(−1, 5)
A′(−5, 1)
A′(5, −1)
A rectangle has a length of 9 millimeters and an
area of 270 square millimeters. What is the width?
What is the perimeter?
Answer:
Step-by-step explanation:
Required width is 30 millimeters & perimeter is 78 millimeters.
Answer:
p=78mm
Step-by-step explanation:
A=l×w
270=9 ×w
270/9=w
w=30mm
P=2(l+w)
p= 2(9+30)
p=78mm
A theater can seat 208 people. The number of rows is 3 less than the number of seats in each row. How many rows of seats are there?
Answer: there are 13 rows of seats in the theater.
Step-by-step explanation: Concurring to the issue, the number of lines is 3 less than the number of seats in each push. So, the number of lines can be communicated as "x - 3".
We know that the theater can situate 208 individuals, so the entire number of seats can be communicated as "x times (x - 3)".
Hence, we are able type in the condition as:
x(x - 3) = 208
Expanding the condition, we get:
x^2 - 3x - 208 =
Presently, ready to unravel this quadratic condition to discover the esteem of "x" which speaks to the number of seats in each push:
Utilizing the quadratic equation:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = -3, and c = -208
x = (-(-3) ± sqrt((-3)^2 - 4(1)(-208))) / 2(1)
x = (3 ± sqrt(841)) / 2
x = (3 ± 29) / 2
Ready to disregard the negative arrangement, so:
x = (3 + 29) / 2
x = 16
Hence, the number of seats in each push is 16.
And, the number of columns can be communicated as "x - 3":
Number of columns = 16 - 3 = 13
6. center (-2, 8), tangent to y = -4
The radius of the circle is 12, and the equation of the circle is:
(x + 2)² + (y - 8)² = 144
What is a circle?
It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
To find the equation of a circle that is tangent to a horizontal line at a given point, we can use the standard form of the equation of a circle:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius.
In this case, the center of the circle is (-2, 8), which gives us:
(x + 2)² + (y - 8)² = r²
To find the radius, we need to know where the circle intersects the y = -4 line. Since the circle is tangent to the line, the distance from the center of the circle to the line is equal to the radius.
The distance between a point (x, y) and a horizontal line y = k is given by |y - k|.
In this case, the distance between the center (-2, 8) and the line y = -4 is |8 - (-4)| = 12.
Therefore, the radius of the circle is 12, and the equation of the circle is:
(x + 2)² + (y - 8)² = 144
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Complete question:
What is the center at (-2, 8), tangent to the line y = -4?
a spherical marble has a volume of 65.45in^3 what is its radius?
Step-by-step explanation:
VOLUME of a SPHERE
4/3 pi r^3 = volume
r = cubrt ( volume / (4/3 pi) ) Plug in the numbers
r = cubrt ( 65.45/ ( 4/3 * pi) = 2.5 inches
You survey students in your class about the number of movies they watched last month. The results are shown in the table.
Required frequency table is
Movie Number of students
1) Action 6
2) Comedy 4
3) Horror 7
4) Drama 5
5) Romance 8
What is frequency table?
A frequency table is a statistical tool used to organize data by counting the number of occurrences of each unique item or value in a dataset. It is a way to summarize and present data in a concise and structured manner, making it easier to understand and analyze.
For example, if you have a dataset of students' grades, you can create a frequency table by listing all the possible grades (e.g., A, B, C, D, F) and counting how many times each grade appears in the dataset. The resulting table will show the frequency or number of times each grade was earned by the students.
Frequency tables can be used to display both qualitative (categorical) and quantitative (numerical) data. For categorical data, the frequency table will show the count or percentage of occurrences of each category. For numerical data, the frequency table will show the number of times each value or range of values appears in the dataset
Based on the data you provided, here is a frequency table for the movie genres:
Movie Number of students
1) Action 6
2) Comedy 4
3) Horror 7
4) Drama 5
5) Romance 8
In the table, the movie genres are listed in the left column, and the number of times each genre appears in the survey results is listed in the right column.
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Correct question is " You survey the students in your class to find out what kinds of movies they like to watch. The students were given the following choices: Comedy (C), Horror (H), Drama (D), Action (A), Romance (R). The following were the results of your survey: C, C, R, R, D, R, H, H, C, A, A, R, A, A, A, R, R, H, H, H, C, H, A, R, D, D, D, D, H, R a. Make a frequency table for the movie genres."
7.24 × 10^4 - 7.21 × 10^3 in scientific notation
[tex]7.24 * 10^4 - 7.21 * 10^3[/tex] in scientific notation is [tex]6.519 * 10^4[/tex].
What is scientific notation?
Scientific notation is a way of expressing a number as a number between 1 and to multiplied by a power of 10.
To subtract these two numbers, we need to make sure they have the same exponent. We can do this by rewriting [tex]7.21 * 10^3[/tex] as [tex]0.721 * 10^4[/tex] (since [tex]7.21 * 10^3 = 0.721 * 10^4[/tex]).
Now we can perform the subtraction:
[tex]7.24 * 10^4 - 0.721 * 10^4 = 6.519 * 10^4[/tex]
Therefore, [tex]7.24 * 10^4 - 7.21 * 10^3[/tex] in scientific notation is [tex]6.519 * 10^4[/tex].
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if L(x) =sinx-cosx, then dxy=?
The derivative of L(x) with respect to x is: d/dx [L(x)] = cosx + sinx
Differentiating the function L(x)Given that
L(x) = sin(x) - cos(x)
To find dy/dx for the function L(x) = sinx - cosx, we need to take the derivative of L(x) with respect to x:
d/dx [L(x)] = d/dx [sinx - cosx]
Using the derivative rules, we can find the derivative of sinx and cosx:
d/dx [sinx] = cosx
d/dx [cosx] = -sinx
Therefore, the derivative of L(x) with respect to x is:
d/dx [L(x)] = cosx + sinx
So, dy/dx for L(x) is cosx + sinx.
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PLEASE HELP!!!! Luke is training for a long-distance bike race. On Tuesday, after riding for 1 hour, he has travelled 5 miles along a straight highway. After 3 hours, he has travelled 17 miles. Write the equation of the line that models Luke’s bike ride. What does the x represent? What does the y represent?
Answer: y=6x-1
Step-by-step explanation:
y=6x-1
x represents the time luke has been riding(hours) and the y represents the distance he has travelled (miles)
Use custom relationships to create a graph, showing the solution region of the system of inequalities, representing the constraints of the situation. Did Mark and label it point represents a viable combination of guest School district is planning a banquet to honor his teacher of the year and raise money for the scholarship foundation. The budget to hold the banquet in a hotel room and miles is $3375 the venue can hold no more than 125 guest the cost is $45 per adult but only $15 per student because caterer offers a student discount discount
We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.
What is banquet?
A banquet is a large formal meal that usually involves multiple courses and is served to a group of people on special occasions such as weddings, awards ceremonies, or fundraising events. Banquets often include speeches, presentations, and entertainment, and are typically held in a large venue such as a hotel ballroom, banquet hall, or conference center. Banquets can be hosted for a variety of purposes, such as to honor a special guest, celebrate an achievement, or raise money for a charitable cause.
To create a graph showing the solution region of the system of inequalities representing the constraints of the situation, we can use custom relationships to define the variables and constraints.
Let's define the variables:
Let x be the number of adult guests.
Let y be the number of student guests.
Now, let's write the system of inequalities representing the constraints of the situation:
The total number of guests cannot exceed 125: x + y ≤ 125
The cost of hosting the banquet cannot exceed $3375: 45x + 15y ≤ 3375
To graph this system of inequalities, we can plot the boundary lines of each inequality and shade the region that satisfies all the constraints.
The boundary lines of each inequality are:
x + y = 125 (the line that connects the points (0, 125) and (125, 0))
45x + 15y = 3375 (the line that connects the points (0, 225) and (75, 0))
To find the viable combinations of guests that satisfy all the constraints, we need to shade the region that is below the line x + y = 125 and to the left of the line 45x + 15y = 3375.
The resulting graph should look like this:
The point where the two lines intersect, (75, 50), represents the maximum number of adult guests (75) and the maximum number of student guests (50) that can be invited to the banquet while staying within the budget and venue capacity. Any point within the shaded region represents a viable combination of guests.
We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.
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A kite frame consists of two perpendicular pieces of wood placed along the diagonals. Decorative binding will be placed along the perimeter of the kite. To the nearest tenth of an inch, how much binding is needed?
a 70.0 in.
b 90.4 in.
c. 100.7 in.
d 140.0 in.
Which is NOT the same as asking:
What is the logarithm of 1,296 if the base is 6?
Answer:
In the equation q^6=1296, what is q
Step-by-step explanation:
If we rewrite the log of 1296 with a base 6 in the exponential form, we get
[tex]6^x=1296[/tex]
When we rewrite q^6 = 1296 in the logarithm form, we get log of 1296 with a base of q. Because the base is no longer 6, this is the wrong answer.
The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and the breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, th
e area is increased by 67 square units. Find the length and breadth of the rectangle.
Answer:
length = 17; breadth = 9
Step-by-step explanation:
Let x = area of rectangle; a = length; b = breadth.
+) a × b = x (1)
+) (a - 5) × (b + 3) = x - 9 => x = ab + 3a - 5b - 15 + 9 (2)
+) (a + 3) × (b + 2) = x + 67 => x = ab + 2a + 3b + 6 - 67 (3)
Replace (1) into (2) & (3):
[tex]\left \{ {{3a - 5b=6} \atop {2a+3b=61}} \right. = > \left \{ {{a=17} \atop {b=9}} \right.[/tex]
Is 3/5 greater than 3/4
Answer:
no, 3/4 is bigger because 3/5 is cut into more pieces then 3/4
Step-by-step explanation:
In parallelogram QRST,
What is
n/Q=33°.
m/T?
In parallelogram QRST, if n/Q=33°, m∠T = 33°.
Why is m∠T = 33° in the parallelogram?In a parallelogram, opposite angles are congruent. When opposite angles are congruent, it means that the angles located on opposite corners of a shape are equal in measure. This is true for several types of shapes, including parallelograms, rectangles, and squares.
Since we know that ∠Q has a measure of 33°, the opposite angle (∠T) will also have the same measure. Therefore, m∠T = 33°.
Congruent opposite angles are important in geometry because they allow us to determine other angles or side lengths of a shape through the use of angles relationships and congruence.
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Measure angle of A equals 32°, b= 15, a=_?_ (Round answers to the nearest hundredth.)
The length of the side a for the triangle ∆ABC is equal to 9.4 to the nearest tenth tenth using the sine rule.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side.
We shall first evaluate for the angle m∠B and then solve for the e using the sine rule as follows:
m∠B = 180° - (32 + 90) {sum of interior angles of a triangle}
m∠B = 58°
a/sin32 = 15/sin58
a = (15 × sin32)/sin58 {cross multiplication}
a = 9.3730
Therefore, the length of the side a for the triangle ∆ABC is equal to 9.4 to the nearest tenth tenth using the sine rule.
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We have 2 squares. One square is shaded 2/12 and the other shaded square in the diagram is 2/15 shaded. How much of the total diagram is shaded?
A.0.148
B.0.148 repeated
C. 0.3
D.0.3 repeated
The correct answer is C. 0.3, which is equivalent to 3/10.
What are fractions?
A fraction is a mathematical representation of a quantity that expresses a part of a whole or a ratio between two quantities.
To find the total fraction of the diagram that is shaded, we need to add the fractions representing the shaded areas of the two squares.
Given that one square is shaded 2/12 and the other shaded square is 2/15, we can add these fractions:
2/12 + 2/15
To add fractions, we need to find a common denominator. The least common multiple (LCM) of 12 and 15 is 60, so we can use 60 as the common denominator for both fractions:
(2/12) + (2/15) = (2/12) * (5/5) + (2/15) * (4/4)
= 10/60 + 8/60
Now we can add the numerators:
= (10 + 8)/60
= 18/60
= 3/10
So, the total fraction of the diagram that is shaded is 3/10.
Hence, the correct answer is C. 0.3, which is equivalent to 3/10.
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Is (5,9) a solution to this system of equations?
Answer:
I D K
Step-by-step explanation:
Please help me and Tysm <3 :)
Answer:
20
Step by step explanation
17+8+36+32+9+11+20+18+29+13+16+31
12
=240
12
=20
Please help I’m confused
The intersection points in the function is (-4, 61)
What is the points of intersection to the functionTo find the intersection points of two functions, we can set them equal to each other and solve for x. Substituting x = -4, we have:
4(-4)² + 3(-4) + 3 = (-4)³ + 7(-4)² - 3(-4) + d
Simplifying, we get:
64 - 12 + 3 = -64 + 112 + 12 + d
d = -77
So the two functions intersect at x = -4 and y = 61. Therefore, the only intersection point is (-4, 61).
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What’s the greatest common factor of 42 and 50:(8 different answers)
Answer:
Step-by-step explanation:
The GCF of 42 and 50 is 2.
In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving AC > EF, given BC = EF. Upload the entire proof below.
Given:
BC = EF
Prove:
AC > EF
STATMENT REASON
1. 1.
2. 2. Betweenness
3. AC > BC 3.
4. 4.
The given information and the transitive property of inequalities, we can prove that [tex]AC[/tex] is greater than [tex]EF[/tex] .
What is the transitive property of inequalities?Statement Reason
[tex]BC = EF[/tex] Given
Betweenness Given
[tex]AC > BC[/tex] Given
[tex]AC > EF[/tex] Transitive property [tex](3, 1)[/tex]
Explanation:
[tex]BC = EF[/tex] Given: Given statement that BC is equal to EF.
Betweenness Given: Given statement that states the concept of betweenness, where BC is between AC and EF.
AC > BC Given: Given statement that [tex]AC[/tex] is greater than BC.
[tex]AC > EF[/tex] Transitive property: Using the transitive property, we can conclude that [tex]AC[/tex] is greater than EF (based on statement 3 and 1).
Therefore, using the given information and the transitive property of inequalities, we can prove that AC is greater than [tex]EF[/tex] .
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Briana helps her mother make a quilt The quilt is 6 feet wide and 12 feet long
Briana and her mother will need to measure and cut the fabric for the quilt. They will need to decide on a pattern and color scheme for the quilt. They will need to sew the pieces of fabric together to create the quilt top. They will need to layer the quilt top with batting and backing fabric and then quilt the layers together. Finally, they will need to bind the edges of the quilt.
If x = 2i is one of the root, find all possible roots of the polynomial f(x) = 2x4-4x3+7x2-4x-4.
The other three roots of the polynomial are:
1) -2i
2) 1 + i
3) 1 - i
The polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4
What are Polynomials?Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.
3x+2x-5, for example, is a polynomial.
Given the polynomial function below
F(x)=x³-x² + 4x-4
Group
F(x)=(x³-x²) + (4x-4)
f(x) = x²(x-1)+4(x-1)
f(x) = (x²+4)(x-1)
If f(x) = 0
x²+4 = 0 and x -1. = 0
x² = -4 and x = 1
x = ±2i and -1
Hence polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4
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complete question:
Which of the following options is a polynomial with a root 2i and exactly 2
real roots?
A. F(x)=x²-x²³ +2x² - 4x-8
B. F(x)=x²-x² + 4x-4
C. F(x)=x²-x³-6x² +4x+8
OD. F(x)= x³ + x² + 4x+8