Answer:
6 5/12 and 5 1/30
Step-by-step explanation:
Just simplify both sides of the equation.
1 3/4 + 1/6 + x = 7 1/2 ---> 1 11/12 + x =7 1/2
then subtract the 1 11/12 from both sides
x = 6 5/12
Last week, Riley worked 7.5 hours per day for 3 days and earned a total of $306.45.
What was Riley's hourly rate of pay last week?
Answer:
13,62$
Step-by-step explanation:
The total hours Riley worked last week: 7.5*3= 22.5 (hours)
Riley's hourly rate of pay: 306.45/ 22.5= 13.62$
Please help
Mishka is on a long road trip, and she averages 60 mph for 2 hours while she's driving on the highway. While she's driving on side roads for 1 hour, she only averages 35 mph. What is the total distance that she covers on her road trip?
A.
59 miles
B.
155 miles
C.
190 miles
D.
95 miles
Let \( l=\int_{0}^{2} \frac{1}{(\alpha+1)^{4}} d x \), The approximation of \( l \) using the two-point Gaussian quadratare foramula is: \[ 0.644628 \] \( 0.248521 \) None of the choices \( 0.133092 \
The correct approximation for the integral is option D. 0.133092.
How did we get the value?To approximate the integral l using the two-point Gaussian quadrature formula, we need to find the weights and abscissae for the formula. The two-point Gaussian quadrature formula is given by:
\( approx w_1f(x_1) + w_2f(x_2) \\
where \: w_1 \: and \: w_2 \: are \: the \: weights \: and \: x_1 \: and \: x_2 \: are \: the \: abscissae.\)
For a two-point Gaussian quadrature, the weights and abscissae can be found from a pre-determined table. Here is the table for two-point Gaussian quadrature:
\(\[
\begin{array}{|c|c|c|}
\hline
\text{Abscissae} (x_i) & \text{Weights} (w_i) \\
\hline
-0.5773502692 & 1 \\
0.5773502692 & 1 \\
\hline
\end{array}
\]
\)
To use this formula, we need to change the limits of integration from 0 to 2 to -1 to 1. We can do this by substituting x = t + 1 in the integral:
\(\[
l = \int_{0}^{2} \frac{1}{(\alpha+1)^{4}} dx = \int_{-1}^{1} \frac{1}{(t+2)^{4}} dt
\]\)
Now, we can approximate the integral using the two-point Gaussian quadrature formula:
\(\[
l \approx w_1f(x_1) + w_2f(x_2) = f(-0.5773502692) + f(0.5773502692)
\]
\)
Substituting the values:
\(\[
l \approx \frac{1}{(-0.5773502692+2)^{4}} + \frac{1}{(0.5773502692+2)^{4}}
\]
\)
Calculating this expression gives:
\(\[
l \approx 0.133092
\]
\)
Therefore, the correct choice is
\(0.133092.\)
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John decides to take his friends to the movies. Let y represent the total amount he spends on the tickets and snacks. Let x represent the number of tickets he buys. Suppose that x and y are related by the equation 12 x plus 18 equals y .
How much does John spend on snacks?
Answer:
y=12x+18
$18
Step-by-step explanation:
what is the slope of a line containing points (2,-1) (3,5)
Answer:
slope(m)=6
Step-by-step explanation:
(2 , -1)=(x1 , y1)
(3 , 5)=(x2 , y2)
use formula : y2 - y1/x2 - x1
=5-(-1)/3-2
=5+1/1
=6/1
=6
therefore slope of a line is 6.
which of the following can be added without altering any of the fractions?
a. 3x/x-1 + 8/x-1
b. 6x+1/4x-8 + 1/4x+1
c. 6x/x+6 + 6x/x-6
d. 6x/x-7 + x-7/6x
Answer:
a
Step-by-step explanation:
\(\frac{3x}{x-1}\) + \(\frac{8}{x-1}\)
These fractions have a common denominator and so do not require to be altered.
The numerators can be added to simplify, that is
= \(\frac{3x+8}{x-1}\)
The remaining fractions have different denominators and would require to be altered before they could be added.
The mapping diagram shows a functional relationship.
A mapping diagram shows a relation, using arrows, between domain and range for the following ordered pairs: (8, 4), (negative two-thirds, 3), (11, negative 1), (4, one-half).
Complete the statements.
f(4) is
1/2
.
f(x) = 4 when x is
.
f(4) is 1/2 then the function f(x) = 4 when x is 8.
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
Given that Using arrows, between domain and range for the following ordered pairs: (8, 4), (- two-thirds, 3), (11, negative 1), (4, 1/2).
Given that
f(4) is 1/2
f(x) = 4 when x is 8
Function of function, as the name suggests, are functions applied over functions themselves which is also called function composition.
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I WILL MARK AS BRAINLIEST
Answer:
B
Step-by-step explanation:
B
Answer:
The answer is B.
Step-by-step explanation:
Plz mark as brainliest I only have one and need 4 more to reach the next rank. If you would, that would help me greatly.
A Mika rode her bike around a trail in the park.
The trail is 3 miles long. Mika rode around the
trail 4 times. How many miles did she travel in all?
Answer:
12 miles
Step-by-step explanation:
Total miles = Length of trail ×
Number of times she rode
Total miles = 3 miles × 4 times
Total miles = 12 miles
Mika traveled a total of 12 miles.
Toni can carry up to 18 lb in her backpack. Her lunch weighs 1 lb, her gym clothes way 2 lb, and her books (b) weigh 3 lb each. how many books can she carry in her backpack?
Answer:
Toni can carry a total of 5 books.
Step-by-step explanation:
\(1+2+3b\leq18\) - Write the inequality out .
\(3+3b\leq 18\) - Combine like terms.
\(3b\leq 15\) - Subtract 3 from both sides .
\(b\leq 5\) - Divide both sides by 3.
She can carry a max of 5 books.
Hope this helps!
A concrete mason has a scale drawing of a rectangular retaining wall. The scale from the retaining wall to the drawing is 8ft to 1in.
the rectangles number things are 10.25 and 2.75
Answer: 1,920ft
Step-by-step explanation:
we concluded that for homes in the city where the data were collected, there is not a statistically significant difference between homes on corner lots and homes on non-corner lots. what was the p-value used that allowed us to make this conclusion? answer with two (or more) decimal places.
In order to provide the specific p-value used to make the conclusion, I would need access to the data or the statistical analysis that was conducted. Without that information, I cannot determine the exact p-value used in your analysis.
However, in general, the p-value is a measure of the strength of evidence against the null hypothesis in a hypothesis test. It represents the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming the null hypothesis is true.
Typically, in statistical analyses, a significance level (alpha) is predetermined, often set at 0.05 (or 5%). If the calculated p-value is less than the significance level, it is considered statistically significant, and the null hypothesis is rejected in favor of the alternative hypothesis. Conversely, if the p-value is greater than the significance level, it is not statistically significant, and the null hypothesis is not rejected.
Therefore, to determine the specific p-value used in your analysis and the conclusion made, you would need to refer to the statistical output or the results of the hypothesis test conducted. The p-value should be reported alongside the statistical analysis, allowing for an accurate interpretation and conclusion regarding the difference between homes on corner lots and non-corner lots.
It is important to note that the p-value should be reported with two or more decimal places to provide a precise indication of the strength of evidence against the null hypothesis.
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Can u guys help me please
Answer:
y=3/4x+3
Step-by-step explanation:
a cell phone box in the shape of a rectangular prism is shown. the height of the box is 4 cm. the height of the original box will be increased by 3.5 centimeters so a new instruction manual and an extra battery can be included. which is closest to the total surface area of the new box?
The closest value to the total surface area of the new box is 275 cm².
To find the surface area of the new box, we need to first calculate the dimensions of the box. Since the original box is a rectangular prism, it has three dimensions - length, width, and height.
Let's assume that the length and width of the box remain the same and only the height changes. So, the new height of the box will be 4 + 3.5 = 7.5 cm.
To calculate the surface area of the new box, we need to find the area of each face and add them up. The box has six faces - two rectangles for the front and back, two rectangles for the sides, and two rectangles for the top and bottom.
The area of each rectangle can be found by multiplying its length and width. Since we know the height and one other dimension (either length or width) of the box, we can use those dimensions to calculate the other dimension using the formula for the volume of a rectangular prism: V = lwh.
Let's assume that the length of the box is 8 cm and the width is 5 cm (these are just arbitrary numbers). Then, the area of each face is:
- Front and back: 8 cm x 7.5 cm = 60 cm² x 2 = 120 cm²
- Sides: 5 cm x 7.5 cm = 37.5 cm² x 2 = 75 cm²
- Top and bottom: 8 cm x 5 cm = 40 cm² x 2 = 80 cm²
The total surface area of the new box is the sum of these areas, which is 120 + 75 + 80 = 275 cm².
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Judah has a dartboard with equally sized spaces numbered 1-20. What is the probability that his first dart
lands on a number less than 9?
Answer:
Below
Step-by-step explanation:
There are EIGHT numbers less than 9 out of the twenty spaces
each has the same probability of getting the dart
eight out of twenty = 8/20 = 2/5
Solve the inequality:
2x+5 < x-1/4
Answer:
x<-3
Step-by-step explanation
2x+5<x-1/4
in x-1/4 you should remove 4 so you should multiply 4 from both side
8x+20<x-1
subtract x from both side
8x-x<-1-20
7x<-21
divided by 7 from both side
x<-3 answer is x<-3
The ordinate of a point is twice its abscissa . If its distance from the point (4,3) is √10 units ,then the coordinates of the point are ?
Answer:
(1 , 2) and (3 , 6)
Step-by-step explanation:
the point P : (x , y) -> (x , 2x) ... ordinate of P point is twice its abscissa, y = 2x
√10 = √(x-4)² + (2x-3)²
5x² - 20x + 25 = 10
x² - 4x + 3 = 0
(x-1)(x-3) = 0
x = 1 or x = 3
y = 2 or y = 6
What is the measure of angle x?
Answer:
35°
Step-by-step explanation:
Step-1) To determine the measure of the unknown angle (x°), We need to determine the sum of the interior angles of the triangle. This can be done by using the formula "180(n - 2), where n = number of sides of the polygon".
⇒ 180(3 - 2) ⇒ 180(1) ⇒ 180°Step-2): Now we know the sum of the interior angles of the triangle, we can add all the angles of the triangles and compare it with 180.
⇒ Sum of interior angles of triangle = 180°⇒ 93° + 52° + x° = 180°Step-3): Finally, we can solve for x. Just isolate the x-variable on the other side of the equation and identify its angle measure.
⇒ 93° + 52° + x° = 180°⇒ 93° + 52° + x° - 93° - 52° = 180° - 93° - 52° ⇒ x° = 180° - 93° - 52° = 35°Therefore, the measure of angle x is 35°.
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1 point Two sides of a triangle have side lengths of 22 inches and 34 inches. What is the range of possible lengths for the third side? *
a snack food company is developing a new flavor for crackers and asks customers to text their preference between two possibilities. what kind of sampling is being used
The kind of sampling that is being used by the snack food company, which is developing a new flavor for crackers and which asks customers to text their preference between two possibilities, is known as non-probability sampling.
Non-probability sampling refers to a sampling technique where a researcher selects samples that are based on the subjective judgment of the researcher rather than random selection. This kind of sampling is a less stringent method, and the method depends heavily on the expertise of the researchers.
Non-probability sampling is carried out by observation, and it is used widely for qualitative research.
Since the food company selects only samples that the company would like (the samples being the company's own customers), the company uses non-probability sampling.
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The area of a rectangle is 90 square inches. Find the length and width so that the rectangle has the least perimeter. Assume that the length and width are both whole numbers
ncmmkksms ndsjms sks dnc dd jdjsks sbds
jdsfjsfjsdj jsdf jsgd jj ej jjs sejr
Can someone please help ?!
Answer:
4 * pi
Step-by-step explanation:
Given r = 10
Formula for the circumference of this full circle is:
2 * r * pi
2 * 10 * pi = 20 * pi
Given one (biggest) part = 16 * pi of this circle.
The other (smaller) part must therefore be:
20 * pi - 16 * pi
4 * pi
Someone please help me with this
Answer:
<4
Step-by-step explanation:
|54| Evaluate absolute value
Answer:
54
Step-by-step explanation:
Think of the I as a car wash and negative numbers as dirty cars and positive numbers as clean cars, if you put a dirty car in a car wash it will come out clean meaning.....
I-1I = 1
In this case we have positive 54 and if you put a clean car in a car wash it will remain clean therefore....
I54I = 54
= 54
Hope this helps.
A slab 150 PCF concrete is to be poured 20 feet above an existing floor at depth of 6 inches at a temp of 90 degrees and a pure rate of 10 feet per hour. what is the expected VERTICAL load? a) 943.333 PSF b) 943.333 PCF c) 150 PSF d) 75 PCF e) 75 PSF
The correct answer to the question is option d) 75 PCF.
To calculate the expected vertical load, we need to consider the weight of the concrete slab and the additional load due to the concrete's temperature and pouring rate. The weight of the slab can be calculated by multiplying the density of the concrete (150 PCF) by the depth (6 inches) and the area (1 square foot). This gives us a weight of 75 pounds per square foot (PSF).
The temperature and pouring rate do not directly affect the vertical load. The temperature and pouring rate are factors that may affect the structural integrity of the slab or the time it takes for the concrete to fully cure. However, they do not contribute to the actual load borne by the slab itself. Therefore, the correct answer is 75 PCF, as it represents the weight of the concrete slab alone.
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consider the 22-parallelepiped in ℝ4r4 defined by the vectors ⃗ 1=⎡⎣⎢⎢⎢⎢133−3⎤⎦⎥⎥⎥⎥and⃗ 2=⎡⎣⎢⎢⎢⎢021−3⎤⎦⎥⎥⎥⎥. v→1=[133−3]andv→2=[021−3]. what is the 22-volume (area) of this?
The 22-volume (area) of the parallelepiped defined by the vectors \(\(\vec{v_1} = [1, 3, 3, -3]\)\) and \(\(\vec{v_2} = [0, 2, 1, -3]\)\) in \(\(\mathbb{R}^4\)\) is 7.
The 22-volume of a parallelepiped in \(\(\mathbb{R}^4\)\) is calculated using the scalar triple product. Let \(\(\vec{v_1}\) and \(\vec{v_2}\)\) be two vectors defining the parallelepiped. The 22-volume (area) of the parallelepiped is given by the magnitude of the scalar triple product of \(\(\vec{v_1}\), \(\vec{v_2}\)\), and their cross product \(\(\vec{n}\)\) (normal vector to the parallelepiped), divided by the magnitude of \(\(\vec{n}\)\).
To calculate the scalar triple product, we find the cross product of \(\(\vec{v_1}\) and \(\vec{v_2}\)\):
\(\(\vec{n} = \vec{v_1} \times \vec{v_2}\).\)
Next, we calculate the scalar triple product:
\(\(V = |\vec{v_1} \cdot \vec{v_2} \times \vec{n}| / |\vec{n}|\).\)
In this case, the cross product \(\(\vec{n}\) of \(\vec{v_1}\) and \(\vec{v_2}\)\) is [-7, 3, -2, -2]. The scalar triple product is \(\(V = |(-1) \cdot (-2) \cdot (-2) \cdot (-2)| / |(-7, 3, -2, -2)| = 7\)\).
Therefore, the 22-volume (area) of the parallelepiped is 7.
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HCF of 10125 and 7425
The HCF of 10125 and 7425 is 675, obtained by prime factorization and identifying the common factors.
To find the highest common factor (HCF) of 10125 and 7425, we can use the method of prime factorization.
Step 1: Prime factorize both numbers.
10125 = 3 × 3 × 3 × 5 × 5 × 5 × 3
7425 = 3 × 3 × 3 × 5 × 5 × 11
Step 2: Identify the common prime factors.
The common prime factors between 10125 and 7425 are 3 and 5.
Step 3: Find the minimum exponent for each common prime factor.
The minimum exponent for 3 is 3 (from 10125) and 3 (from 7425).
The minimum exponent for 5 is 3 (from 10125) and 2 (from 7425).
Step 4: Multiply the common prime factors raised to their minimum exponents.
HCF(10125, 7425) = 3^3 × 5^2 = 27 × 25 = 675.
Therefore, the highest common factor of 10125 and 7425 is 675.
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pleaseee HELPPP will mark Brainly
Find x and length of KE.
KE=4x+5
EM=6x-1
Find KE
Answer:
KE=17
Step-by-step explanation:
X=3
12+5=17
18-1=17
hope this helps :)
Answer:
KE length: 17
x = 3
Step-by-step explanation:
In this, the length of KE and EM should be the same. So we can put the numbers we have into an equation:
4x + 5 = 6x - 1
Then we just simplify
1 + 5 = 6x - 4x
6 = 2x
x = 3
Now we should find the length of KE with the expression used for KE:
4(3) + 5
12 + 5
17
Therefore, the length of KE is 17
Please Help me - You will get 60 points for the rapid reply- Use isosceles trapezoid ABCD to determine the following measurements-
Answer:
1) AD = 9 in
2) DE = 9.25 in
3) ∠EDC = 36°
4) ∠AEB = 108°
5) 11.5 in
Step-by-step explanation:
1) AD = BC = 9in
2) AC = BD (diagonals are equal)
⇒ BD = 14.25
⇒ BE + DE = 14.25
⇒ 5 + DE = 14.25
DE = 9.25
3) Since AB ║CD,
∠ABE = ∠EDC = 36°
4) ∠ABE = ∠BAE = 36°
Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)
⇒ 36 + 36 + ∠AEB = 180
∠AEB = 108
5) midsegment = (AB + CD)/2
= (8 + 15)/2
11.5