The amount of stone in each sidewalk is 3/16
How to determine the amount of stone in each sidewalk?The given parameters are
Stones = 3/4 tons
Side walks = 4
The amount of stone in each sidewalk is calculated using
Amount = Stones/Side walks
Substitute the known values in the above equation
Amount = 3/4 / 4
Evaluate the quotient
Amount = 3/16
Hence, the amount of stone in each sidewalk is 3/16
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If X = 2 centimeters, Y = 5 centimeters, and Z = 5 centimeters, what is the area of the object?
Answer: [tex]35 cm^2[/tex]
Step-by-step explanation:
Area of trapezium =
2X = 2 + 2 = 4 cm
2Z = 5 + 5 = 10 cm
Y = 5 cm
[tex]\dfrac{ \left( 4+10 \right) }{ 2 } \times 5[/tex]
|
|--------> 35 [tex]cm^2[/tex]
Geometry question need help finding the answer.
Answer: 1208.96
Step-by-step explanation:
The volume of the cylinder is [tex](\pi)(4^2)(4)=64\pi[/tex]
The volume of the prism is [tex](6)(12)(14)=1008[/tex]
So, the total volume is [tex]1008+64\pi=\boxed{1208.96}[/tex]
A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,320 ft Determine the flag's width and length if the length is 400 ft
greater than the width.
The flag's width is
_? ft. Its length is
_? ft.
Answer: 380 ft and 780 ft
Step-by-step explanation:
We can assume that the flag is a rectangle. If the width of the flag is w, then the length is w + 400.
The formula for the perimeter of a rectangle is [tex]2(l+w)[/tex]. Let's plug in the values we know.
[tex]P=2(l+w)\\2320=2(w+400+w)\\1160=2w+400\\760=2w\\w=380[/tex]
We know that the length is 400 more than the width, so let's find the length.
[tex]l=w+400\\l=380+400=780[/tex]
Hence, the flag's width is 380 ft and the length is 780 ft.
Use the definition of a Taylor series to find the first three non zero terms of the Taylor series for the given function centered at a=1. Write the Taylor series in summation notation
Answer:
[tex]e^{4x}=e^4+4e^4(x-1)+8e^4(x-1)^2+...[/tex]
[tex]\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n[/tex]
Step-by-step explanation:
Taylor series expansions of f(x) at the point x = a
[tex]\text{f}(x)=\text{f}(a)+\text{f}\:'(a)(x-a)+\dfrac{\text{f}\:''(a)}{2!}(x-a)^2+\dfrac{\text{f}\:'''(a)}{3!}(x-a)^3+...+\dfrac{\text{f}\:^{(r)}(a)}{r!}(x-a)^r+...[/tex]
This expansion is valid only if [tex]\text{f}\:^{(n)}(a)[/tex] exists and is finite for all [tex]n \in \mathbb{N}[/tex], and for values of x for which the infinite series converges.
[tex]\textsf{Let }\text{f}(x)=e^{4x} \textsf{ and }a=1[/tex]
[tex]\text{f}(x)=\text{f}(1)+\text{f}\:'(1)(x-1)+\dfrac{\text{f}\:''(1)}{2!}(x-1)^2+...[/tex]
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}[/tex]
[tex]\text{f}(x)=e^{4x} \implies \text{f}(1)=e^4[/tex]
[tex]\text{f}\:'(x)=4e^{4x} \implies \text{f}\:'(1)=4e^4[/tex]
[tex]\text{f}\:''(x)=16e^{4x} \implies \text{f}\:''(1)=16e^4[/tex]
Substituting the values in the series expansion gives:
[tex]e^{4x}=e^4+4e^4(x-1)+\dfrac{16e^4}{2}(x-1)^2+...[/tex]
Factoring out e⁴:
[tex]e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right][/tex]
Taylor Series summation notation:
[tex]\displaystyle \text{f}(x)=\sum^{\infty}_{n=0} \dfrac{\text{f}\:^{(n)}(a)}{n!}(x-a)^n[/tex]
Therefore:
[tex]\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n[/tex]
How do I solve it I am running low on time it says it wrong don’t know
x > 1 is the required solution of the given inequality - 3x + 7 < 4. This can be obtained by solving the inequality the same way as we solve an algebraic equation.
Solve the inequality:The inequality can be solved as the same way as we solve an algebraic equation.
Combine the terms with variables to one side and constants to other side.To multiply the whole inequality with negative terms we reverse the sign of the inequality.Here in the question the inequality to be solved is given:
- 3x + 7 < 4
By subtracting 7 from both sides of the inequality we get,
⇒ - 3x + 7 - 7 < 4 - 7
⇒ - 3x < - 3
To make the side of the inequality with variable x positive we multiply the whole equation with - 1, then we have to reverse the sign of inequality since we have to multiply the whole inequality with a negative term,
we get,
⇒ 3 x > 3
Now finally by dividing the whole inequality by 3 we get,
⇒ x > 1
The number line representation can be done by marking values from 1 to numbers greater than 1.
Hence x > 1 is the required solution of the given inequality - 3x + 7 < 4.
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Paulo wants to buy new carpet for his bedroom. The floor is in the shape of a rectangle. Its length is 16 feet and its width is 11 feet. The carpet he wants costs $9 per square foot. How much will the carpet cost for the floor?
Answer:
11x9=99 16x9=144=243 144+99
The cost of the carpet required for the given rectangular floor is $1584.
A rectangle is a quadrilateral with equal pairs of sides.
Given that:
The shape of the floor is a rectangle.
The length of the floor is 16 feet.
The width of the floor is 11 feet.
So,
The area of the floor = length × breadth
= 16 × 11
= 176 sq feet
The area of the floor is 176 sq feet.
The cost of the carpet for a 1 sq foot floor = $9
The cost of the carpet for a 176 sq feet floor = $9 × 176
= $1584
Thus, the cost of the carpet for a 176 sq feet floor is $1584.
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if you could help with all 4 questions that would be great pls answer if you know the RIGHT answer
Step-by-step explanation:
3. B
because the figure to the left of the y-axis yields the one to the right when you reflect it across y = x.
4. C
Flip either of the figures vertically across x = -1 which is their intersection point and you'll get the other.
5. D
it can't be clockwise because the x value of the vertices would have been negative. so it is 270° counterclockwise resulting in ( -y , x )
6. A
Similar to #4 which except this time, you flip it horizontally like how you lay a book or pick it up.
What is the area of the parallelogram shown above
The area of the parallelogram is 55 square feet
How to determine the area of the parallelogram?From the figure, we have the following dimensions:
Height = 5 ft
Base = 11 ft
The area of the parallelogram is calculated as:
Area = Base * Height
This gives
Area = 5ft * 11ft
Evaluate the product
Area = 55 square feet
Hence, the area of the parallelogram is 55 square feet
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PLEASE HELP ME ASAP! BEING TIMED
If the tens digit of a number is 4 times the units digit and the hundreds digit is twice the tens digit, is the number even or odd?
The number is 841
So we can see that the number is odd.
Is the number even or odd?
Here we have a 3-digit number that can be written as:
a*100 + b*10 + c
Here we know that:
"the tens digit of a number is 4 times the units digit"
b = 4*c
"the hundreds digit is twice the tens digit"
a = 2*b
Now, remember that a, b, and c, are numbers on the set {0, 1, ..., 8, 9}
And if we replace the first equation into the second, we get:
a = 2*(4*c) = 8*c
Now, the only value of c that we can use such that a is a single digit whole number is c = 1
(if c = 0, then our number is zero)
a = 8*1 = 8
b = 4*1 = 4
c = 1
The number is 841
So we can see that the number is odd.
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what is the next word in the pattern below?
Fall, Winter, Spring, Summer, Fall, __, ...
A. Winter
B. Summer
C. Spring
D. Fall
The answer is A. Winter.
As the pattern is : F, W, Sp, Su, F... (letters used for convenience), then the next word in the pattern will be Winter, because that was shown in the previous sequence.
Twelve education students, in groups of four, are taking part in a student-teacher program. Mark cannot be in the first group because he will be arriving late. How many ways can the instructor choose the first group of four education students?.
330 ways can the instructor choose the first group of four education students.
What is probability in math?
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.Given:
12 students
3 groups consisting of 4 students.
Mark can't be in the first group.
The combination formula that I used is = n! / r!(n-r)!
where: n = number of choices ; r = number of people to be chosen.
This is the formula I used because the order is not important and repetition is not allowed.
Since Mark can't be considered in the first group, the value of n would be 11 instead of 12. value of r is 4.
numerator: n! = 11! = 39,916,800
denominator: r!(n-r)! = 4!(11-4)! = 4!*7! = 120,960
Combination = 39,916,800 / 120,960 = 330
Therefore, There are 330 ways that the instructor can choose 4 students for the first group.
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Which of the following are possible measures of the interior angles of a regular polygon? If possible, how many sides does the polygon have: 90°, 100°, 110° 125°,
150°, 175°.
Step-by-step explanation:
180(n-2)/n=90 ( this is the solution for the 90)
cross multiplying
180n-360=90n
180n-90n=360
90n=360
90n/90=360/90
n=4, the number of sides for the polygon with 90° is 4 sides
Solution for 100°
180(n-2)/n=100
180n-360=100n
180n-100n=360
80n=360
80n/80=360/80
n=4.5
Same applies to the rest 110°,125° ,150°,175°
factor (16x^2-8x+1)
Please show your work lol
Answer:
(4x - 1)^2.
Step-by-step explanation:
16x^2 - 8x + 1
Multiplying the first and last coefficients:
16 * 1 = 16
We need 2 numbers whose product is 16 and whose sum is -8.
These are - 4 and -4.
So we now write:
16x^2 - 4x - 4x + 1
Now factor by grouping :
= 4x(4x - 1) - 1(4x - 1)
= (4x - 1)(4x - 1)
= (4x - 1)^2
This method of factoring quadratics is called the 'ac' method - you split the middle term ( in this case the -8x) into 2 parts.
Answer:
[tex](4x-1)^2[/tex]
Step-by-step explanation:
Given quadratic expression:
[tex]16x^2-8x+1[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b:
[tex]ac = 16 \times 1 = 16[/tex][tex]b = -8[/tex]Therefore, two numbers are: -4 and -4
Rewrite the middle term as the sum of these two numbers:
[tex]\implies 16x^2-4x-4x+1[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 4x(4x-1)-1(4x-1)[/tex]
Factor out the common term (4x - 1):
[tex]\implies (4x-1)(4x-1)[/tex]
Apply the exponent rule: aa = a²
[tex]\implies (4x-1)^2[/tex]
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Find the length of the line joining the points A(-2,10) and B(-8,2)
Length of the line
= [tex]\sqrt{((-2)-(-8))^{2}+(10-2)^{2} }[/tex]
= [tex]\sqrt{36+64}[/tex]
=[tex]\sqrt{100}[/tex]
= 10
180 divided in the ratio of 7:3:5
Answer:
Let , the constant factor be x so 3 X + 5 x + 7 x = 180
Step-by-step explanation:
Find out the value of x
7x+3x+5x=180
15x=180
x=180/15
x=12
now,
x=3 multiplied by 12=36
x=7 multiplied by 12=84
x=5 multiplied by 12=60
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how do you simplify (-x^2)^2 ?
Answer:
[tex] {x}^{4} [/tex]
Step-by-step explanation:
[tex] { {( - x}^{2} )}^{2} = ( - {x}^{2} )( - {x}^{2} ) = {x}^{4} [/tex]
An expression is defined as a set of numbers, variables, and mathematical operations. The value of the given expression when simplified is equal to x⁴.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression can be simplified as shown below,
(-x²)²
= (-x × -x)²
Since the product of two negatives is always positive, therefore, we can write,
= -x² × -x²
As per the rule of exponents, the expression can be written as,
= x⁴
Hence, the value of the given expression when simplified is equal to x⁴.
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Question 3 of
Select the correct answer.
A meteorologist observed the temperature in Clarkton over a two-year period. The graph below shows the average monthly
temperature in Clarkton during this period.
The function describing this graph is a transformation of the parent cosine function, y = cos(z).
Which interval is closest to the range of the transformed function ?
With respect to the parent function y = cos x, the interval closest to the range of the transformed function is ( 0,50). the correct option is D.
How to find the functions corresponding to each graph based on the period of a function?Mathematically speaking, cosines are periodic functions, and period (T) is the distance in the horizontal axis such that f(t + T) = f(t). The period of the parent cosine function is 2π. The period in daughter functions may vary by means of the following form:
y = cos Ax (1)
Where:
x - Independent variable
y - Dependent variable
A - Period width
From the graph, it is observed that with respect to the parent function y = cos x, the interval closest to the range of the transformed function is ( 0,50). the correct option is D.
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Answer: The answer is [0,65]
Step-by-step explanation:
Find the surface area of the prism.
full of sand, the wagon weighs 100 pounds. If the wagon weighs 80 ounces when its empty, how much do the bags of sand weigh?
given,
wagon weight with sand = 100 pounds
wangon weight = 80 ounces ÷ 16 = 5 pounds
sand weight = 100 - 5 = 95 pounds//
Which of the following is NOT a monomial? -11x
x - 4
3
22xy
Answer:
x - 4
Step-by-step explanation:
monomial is one term
-11x is only one term
x-4 isn't
3 is one term
22xy is only one term
only x-4 isn't a monomial
An airplane is heading due north at 700 kph, and a wind blows at 60 kph in the direction s 45° e. what is the plane’s ground speed?
We can infer and logically deduce that airplane’s ground speed is equal to 658.94 kph.
Given the following data:
Airplane speed = 700 kph.Wind speed = 60 kph.Angle = 45° due East.What is speed?Speed can be defined as the distance covered by an object per unit of time. Thus, speed can be measured in kilometer per hour (kph).
Mathematically, speed can be calculated by using this formula;
Speed = distance/time
How to calculate the plane’s ground speed?In order to calculate the airplane’s ground speed, we would apply the law of cosine:
C² = A² + D² - 2(A)(D)cosθ
Substituting the given parameters into the formula, we have;
C² = 700² + 60² - 2(700)(60)cos45
C² = 434,203.03
C = √434,203.03
C = 658.94 kph.
In conclusion, we can infer and logically deduce that airplane’s ground speed is equal to 658.94 kph.
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Sarah attempt to convert 8 miles in to kilomiters explain her error and then provide a correct conversion
Answer:
12.8 km
Step-by-step explanation:
each mile has 1.6 km in it so in order to find the total distance in km we need to multiply the miles by 1.6= 8 miles x 1.6 =12.8 km
The motion of an object was recorded by measuring the velocity of the object in meters per second at various times, as shown in the table. The scatterplot below was graphed from the data in the table, where t represents the time, and v represents the velocity.
Based on the scatterplot, which equation BEST represents the relationship between velocity and time?
The regression equation that represents the relationship between velocity and time is:
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points (t,v), that is, time and velocity, are given as follows:
(0, 6.1), (2.1, 12.2), (5.3, 17.4), (8.2, 26.4), (10, 28.1), (12.1, 32.8).
Hence, inserting these points into a calculator, the equation is given by:
v = 2.19t + 6.7.
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State the converses of the following statements. In each case, also decide whether the converse is true or false.
(1) If n is an even integer, then 2n + 1 is an odd integer.
(2) If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.
(3) If each pair of opposite sides of a quadrilateral is equal, then the quadrilateral is a parallelogram.
(4) If the decimal expansion of a real number is terminating, then the number is rational.
Help!
Answer:
See below.
Step-by-step explanation:
Converse
The converse of a statement is formed by switching the hypothesis and the conclusion.
Hypothesis: The part after the "if".Conclusion: The part after the "then".Question 1Given statement: If n is an even integer, then 2n + 1 is an odd integer.
Hypothesis: "n is an even integer"Conclusion: "2n + 1 is an odd integer"Converse: If 2n + 1 is an odd integer, then n is an even integer.
Question 2Given statement: If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.
Hypothesis: "a transversal intersects two parallel lines"Conclusion: "each pair of corresponding angles is equal"Converse: If a transversal intersects two lines such that each pair of corresponding angles is equal, then the two lines are parallel to each other.
Question 3Given statement: If each pair of opposite sides of a quadrilateral is equal, then the quadrilateral is a parallelogram.
Hypothesis: "each pair of opposite sides of a quadrilateral is equal"Conclusion: "the quadrilateral is a parallelogram"Converse: If a quadrilateral is a parallelogram, then each pair of opposite sides of the quadrilateral is equal.
Question 4Given statement: If the decimal expansion of a real number is terminating, then the number is rational.
Hypothesis: "the decimal expansion of a real number is terminating"Conclusion: "the number is rational"Converse: If a real number is rational, then the decimal expansion of the number is terminating.
Matt (180lb male) goes to a party and is served beer in a 16 oz red plastic cup. he has 3 cups of beer over a two hour period. What is Matt's BAC?
Matt's BAC the equation for is mathematically given as
X= 4 standard drinks
This is further explained below.
What is Matt's BAC?Blood Alcohol Content, sometimes known as BAC, is a measurement that expresses the amount of alcohol present in the blood as a percentage. Because it is measured in grams per 100 milliliters of blood, a blood alcohol concentration (BAC) of 0.08 indicates that your blood contains 0.08 percent alcohol by volume.
Generally, One standard drink is equal to twelve ounces of beer.
He drank a total of 48 ounces of beer since he had three cups of beer that were each 16 ounces.
In conclusion, the number of standard drinks that Matt consumed
X= 48/12
X= 4 standard drinks
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1. Use the figure to determine the value of x and y.
Answer:
Step-by-step explanation:
x=100 bc like 180-80=100
y=80 bc vertical angles
Answer:
y = 80*
x = 100*
Step-by-step explanation:
y is the same to the 80* angle and therefore x is 100*
180* - 80 = 100*
MN =7. Find AB.
3.5
10.5
14
The length of line segment AB by observation if the diagram in the task content is; 14.
What is the length of line segment AB?It follows from the task content that the line segment MN can be considered as parallel to line segment AB. This follows from the fact that the vertices of triangle MNO are midpoints of the line segments of triangle ABC.
Consequently, it can be concluded that line segment AB is twice the length of line segment MN and hence, BC = 2 × 7 = 14.
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Figure 2 was constructed using figure 1.
On a coordinate plane, 2 parallelograms are shown. Parallelogram 1 is in quadrant 1 and sits on the x-axis with a point at (0, 0). Parallelogram 2 is in quadrant 4 and sits on the y-axis with a point at (0, 0). Parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.
For the transformation to be defined as a rotation, which statements must be true? Select three options.
The options A, C, E are correct. On the basis of the theory of the rotation and transformation on the parallelogram.
According to the statement
we have given that the
Parallelogram 1 is in quadrant 1 and sits on the x-axis with a point at (0, 0). Parallelogram 2 is in quadrant 4 and sits on the y-axis with a point at (0, 0)
And we have to find that the which terms are corrected from the given options when Parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.
So, For this purpose we know that the
A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.
And According to the given statement
when parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.
Then the conditions A, C, E are applicable because on rotation these things are applicable.
So, The options A, C, E are correct. On the basis of the theory of the rotation and transformation on the parallelogram.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Figure 2 was constructed using figure 1.
On a coordinate plane, 2 parallelograms are shown.
Parallelogram 1 is in quadrant 1 and sits on the x-axis with a point at (0, 0). Parallelogram 2 is in quadrant 4 and sits on the y-axis with a point at (0, 0).
Parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.
For the transformation to be defined as a rotation, which statements must be true? Select three options.
A. The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2).
B. The transformation is rigid.
C. Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.
D.Segment CP is parallel to segment CP'.
E. If figure 1 is rotated 180° about point C, it will be mapped onto itself.
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60. In the given figure, PTR is tangent of a circle. If AT=PT and ZAPT=20°, what is the value of ZABT?
The value of angle ABT is 40 degrees if PTR is the tangent of a circle option (a) 40° is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
It is given that:
A circle is shown in the picture.
PTR is the tangent of a circle.
AT=PT
Angle APT=20°
Let O is the center of the circle:
Angle BOT = 2 Angle PAT = 40 degrees
BO = TO = r
Angle BOT = Angle TBO = (1/2)(180 - 40) = 70 degrees
RTP is the tangent
OT ⊥ PTR
Angle OTA = 90 - Angle ATR = 50 degrees
Angle ABT = 180 - Angle PAT - Angle BTA
= 180 - 20 - (170 + 50)
= 40 degrees
Thus, the value of angle ABT is 40 degrees if PTR is the tangent of a circle option (a) 40° is correct.
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At school, the teacher surveyed the color preferences of 21 students. Out of every
7 students surveyed, 4 said they liked blue the best. How many students said their favorite
color was blue?
Taking into account the definition of proportion, 12 students said their favorite color was blue.
Definition of ratioThe ratio is the comparison of two quantities and is measured from the division of two values. In other words, the ratio between two magnitudes is defined as their ratio or division; that is, given the quantities a and b, the ratio between them is a÷b.
The result of this division can be understood as how many times one quantity is in another.
Definition of proportionThe relationship of equality that exists between two ratios, that is, between two comparisons between two determined quantities, is known as a proportion. So if a/b corresponds to the ratio, then a/b = c/d equals a proportion.
Students that said their favorite color was blueAt school, the teacher surveyed the color preferences of 21 students. Out of every 7 students surveyed, 4 said they liked blue the best. This can be expressed as a proportion as follow:
4÷7= x÷ 21
where x is the number of students of the 21 students surveyed who like blue.
Solving:
(4÷7)×21= x
12= x
Finally, 12 students said their favorite color was blue.
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