#19
\(\\ \sf\longmapsto \dfrac{7}{5}\)
#20
\(\\ \sf\longmapsto \dfrac{9}{5}\)
#21
\(\\ \sf\longmapsto \dfrac{11}{7}\)
#22
\(\\ \sf\longmapsto \dfrac{12}{7}\)
#23
\(\\ \sf\longmapsto \dfrac{2}{2}=1\)
#24
\(\\ \sf\longmapsto \dfrac{3}{2}\)
#25
\(\\ \sf\longmapsto \dfrac{5}{2}\)
#26
\(\\ \sf\longmapsto \dfrac{6}{2}=3\)
#27
\(\\ \sf\longmapsto \dfrac{8}{2}=4\)
#28
\(\\ \sf\longmapsto \dfrac{9}{2}\)
#29
\(\\ \sf\longmapsto \dfrac{13}{4}\)
#30
\(\\ \sf\longmapsto \dfrac{19}{4}\)
#31
\(\\ \sf\longmapsto \dfrac{37}{6}\)
#32
\(\\ \sf\longmapsto \dfrac{25}{6}\)
Answer:
19. 7 to base five => 12
21. 11 to base seven => 14
23. 2 to base two=> 10
25. 5 to base two => 101
27. 8 to base two => 1000
29. 13 to base four => 31
31. 37 to base six => 101
33. 87 to base five => 322
35. 108 to base four => 1230
37. 19 to base two => 10011
The number of hot drinks sold decreases as the weather becomes warmer. What type of correlation does this statement show?
Answer:
Step-by-step explanation:
Ueuehehehhehehehehehehheshehhehehehdhdhdhdhdhhdhdhdhdhdhhdhd
Find the value of x. Write your answer in simplest form.
Answer:
\(x = \frac{9}{ \sqrt{2} } = \frac{9 \sqrt{2} }{2} \)
Solve for the rate (as a %). Round to the nearest tenth of a percent when necessary. What is the rate if the base is 366 and the portion is 50?
Answer:
\(\Huge \boxed{\text{13.66$\%$}}\)
Step-by-step explanation:
To find the rate, we need to use the following formula:
\(\LARGE \boxed{ \boxed{\text{Rate = $\frac{\text{Portion}}{\text{Base}}$$\times$100}}}\)
Where "Portion" is the part of the whole and "Base" is the whole.
Now, let's plug in the given values:
\(\large \text{Rate = $\frac{\text{50}}{\text{366}}$$\times$100 = 13.66 (Rounded to the nearest tenth of a percent)}\)
Therefore, the rate is 13.66% (rounded to the nearest tenth of a percent).
----------------------------------------------------------------------------------------------------------
Write a explicit formula for the given recursive formulas for each arithmetic sequence
9,15,21,27 and 7,0,-7,-14
In arithmetic progression, 9,15,21,27,33,39 is a₅ and a₆ .
What is arithmetic progression?
A series of numbers is called a "arithmetic progression" (AP) when any two subsequent numbers have a constant difference. It also goes by the name Arithmetic Sequence.a₁ = 9
a₂ = 15
a₃ = 21
Notice that a₂ - a₁ = 6 and a₃ - a₂ = 6
We can deduce that aₙ₊₁ = aₙ + 6
We can test this on the 4th term : a₄ should equal 21 + 6 = 27
Since this checks out we can say that the sequence is an arithmetic progression with a common difference of 6.
a₅ = 27 + 5 = 33
and
a₆ = 33 + 6 = 39
7,0,-7,-14
find the common difference by substracting any term in the sequence from the term that comes after it.
a₂ - a₁ = 0 - 7 = -7
a₃ - a₂ = -7 - 0 = -7
a₄ - a₃ = -14 - -7 = -7
the difference of the sequence is constant and equals the difference between two consecutive terms.
d = -7
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PLEASE HELP ME ASAP The average of 16 consecutive odd numbers is 122. Find the smallest odd number. FIRST TO ANSWER GETS BRAINLIEST
Answer:
107
Step-by-step explanation:
Hello, Let's note n the odd number that we are looking for.
If n is odd, n+1 is even but n+2 is odd again and so on and so forth.
So, the 16 consecutive odd numbers are
n, n+2, n+4, ... n+2k, ,,,, ,n+30
It means that the average is:
\(\displaystyle \dfrac{1}{16}(n+(n+2)+...+(n+2k)+...+(n+2*15))\\\\=\dfrac{1}{16}\sum_{k=0}^{k=15} {(n+2k)}\\\\=\dfrac{1}{16}\left(n * 16 + 2 \sum_{k=1}^{k=15} {k} \right)\\\\=\dfrac{1}{16}\left(n * 16 + 2 (\dfrac{15*16}{2}) \right)\\\)
And it must be equal to 122, so we can write.
\(\dfrac{1}{16}\left(n * 16 + 2 (\dfrac{15*16}{2}) \right)=122\\\\n+15=122\\\\n = 122-15=107\)
Thank you.
50 POINTS FIRST GOOD ANSWER GETS BRAINLIEST
Express f(x)=3+|2x-5| as a piecewise function WITHOUT using absolute value
Please give a detailed response not just answer to help me understand
Answer:
\(f(x)=3+|2x-5|=\left\{ \begin{array}{ll} 2x-2& \quad x \geq 5/2 \\ -2x+8 & \quad x < 5/2 \end{array} \right.\)
Step-by-step explanation:
We are given the function:
\(f(x)=3+|2x-5|\)
Remember that by the definition of absolute value:
\(\displaystyle |x|= \left\{ \begin{array}{ll} x & \quad x \geq 0 \\ - x & \quad x < 0 \end{array} \right.\)
Our absolute value is:
\(|2x-5|\)
First, we will find when it becomes 0. Set the equation equal to 0:
\(2x-5=0\)
Solve for x:
\(x=5/2\)
So, we can see that for all values greater than x = 5/2, 2x - 5 is positive.
For all values less than x = 5/2, 2x - 5 is negative.
Therefore (the positive case go above, and the negative case go below):
\(|2x-5|= \left\{ \begin{array}{ll} 2x-5 & \quad x \geq 5/2 \\ -(2x-5) & \quad x < 5/2 \end{array} \right.\)
Finally, we can add a three:
\(f(x)=3+|2x-5|=\left\{ \begin{array}{ll} 3+(2x-5) & \quad x \geq 5/2 \\ 3+(-(2x-5)) & \quad x < 5/2 \end{array} \right.\)
Simplify if desired:
\(f(x)=3+|2x-5|=\left\{ \begin{array}{ll} 2x-2& \quad x \geq 5/2 \\ -2x+8 & \quad x < 5/2 \end{array} \right.\)
The vector ⇀
= ⟨2, 3⟩ is multiplied by the scalar –4. Which statements about the components, magnitude, and direction of the scalar product –4⇀
are true? Select all that apply.
A. The component form of −4⇀
is ⟨–8, –12⟩.
B. The magnitude of −4⇀
is 4 times the magnitude of ⇀
.
C. The direction of −4⇀
is the same as the direction of ⇀
.
D. The vector −4⇀
is in the fourth quadrant.
E. The direction of −4⇀
is 180° greater than the inverse tangent of its components.
Answer:
Therefore, the correct statements are A, B, and E.
Explanation:
Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.
To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀
.
- The component form of −4⇀
is obtained by multiplying each component of ⇀
by –4. Therefore, −4⇀
= ⟨–8, –12⟩. This means that statement A is true.
- The magnitude of −4⇀
is obtained by multiplying the magnitude of ⇀
by 4. The magnitude of ⇀
is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀
is 4√13. This means that statement B is true.
- The direction of −4⇀
is opposite to the direction of ⇀
because the scalar –4 is negative. This means that statement C is false.
- The vector −4⇀
is in the third quadrant because its components are both negative. This means that statement D is false.
- The direction of −4⇀
is 180° greater than the inverse tangent of its components because it is opposite to ⇀
. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀
is 180° + tan^(-1)(3/2). This means that statement E is true.
Therefore, the correct statements are A, B, and E.
please help me out asap
Answer:
\( {(x + 5)}^{2} - {x}^{2} \\ {x }^{2} + 10x + 25 - {x}^{2} \\ 10x + 25 \\ 5(2x + 5)\)
Real numbers a and b satisfy
a + ab = 250
a - ab = -240
Enter all possible values of a, separated by commas.
The only possible value of "a" that satisfies the given equations is a = 5.
The possible values of "a" that satisfy the given equations, let's solve the system of equations:
a + ab = 250 ---(1)
a - ab = -240 ---(2)
We can solve this system by using the method of substitution. Rearranging equation (2), we get:
a = ab - 240 ---(3)
Substituting equation (3) into equation (1), we have:
(ab - 240) + ab = 250
2ab - 240 = 250
2ab = 250 + 240
2ab = 490
ab = 490/2
ab = 245
Now we have the value of "ab."
We can substitute this back into equation (3) to solve for "a":
a = (245) - 240
a = 5
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Each of the following describes a variable expression.
1. The area of a rectangle that is (x + 2) units long and 4 units wide.
4(x + 2)
2. The perimeter of a rectangle that is (x + 3) units long and (x + 1) units wide.
2(x + 3) + 2(x + 1)
3.
The volume of a rectangular prism that is 2 units long, 1 unit wide, and (2x + 4) units high.
2(1)(2x + 4)
which two are equivalent
Both equations are equal since they both reduce to 4x + 8 as the surface area of a rectangle with dimensions of (x + 2) units and (4 units).
what is expressions ?An expression in mathematics is made up of various elements, including numbers, variables, and mathematical operations like addition, subtraction, multiplication, division, exponents, and roots. Expressions can represent a single number or a group of numbers, and they can be simple or sophisticated. For instance, the phrase 3x + 2 denotes a linear equation with the variable x. The expression (x + 3)(x - 4) denotes the sum of two binomials.
given
First and third expressions are interchangeable.
the surface area of a rectangle with dimensions of (x + 2) units and (4 units).
Area is equal to length times breadth.
Area = 4x + 8x + (x + 2) x 4a rectangular prism with dimensions of 2 units long, 1 units broad, and (2x + 4) units high has a volume of 4 units.
Volume is calculated using the formula LWH.
Volume equals 2 x 1 x ((2x + 4))
Volume equals 2(2x + 4)
Volume = 4 times Plus 8
Both equations are equal since they both reduce to 4x + 8 as the surface area of a rectangle with dimensions of (x + 2) units and (4 units).
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Find the missing numbers
Based on the information provided, the missing number would be number 6.
How to find the missing numbers?When it comes to finding missing numbers, the first step is to decipher or identify the pattern. This can be either a sequence of numbers or the application of a specific mathematical operation such as subtraction or addition.
In this case, we can see there is a sequence of numbers that seems to go from 1 to 9. However, if you check carefully, the number 6 is missing, which is the number you need to add.
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the shortest side of a right triangle measures 7m. The lengths of the other two sides are Consecutive integers. What is the length of the other two sides?
The lengths of the other two sides of the right triangle are 24m and 25m, respectively.
Let's assume the consecutive integers representing the lengths of the other two sides of the right triangle are x and x + 1, where x is the smaller integer. We are given that the shortest side measures 7m. Now, we can use the Pythagorean theorem to solve for the lengths of the other two sides.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Using this theorem, we have the equation:
\(7^2 + x^2 = (x + 1)^2\)
Expanding and simplifying this equation, we get:
\(49 + x^2 = x^2 + 2x + 1\)
Now, we can cancel out \(x^2\) from both sides of the equation:
49 = 2x + 1
Next, we can isolate 2x:
2x = 49 - 1
2x = 48
Dividing both sides by 2, we find:
x = 24
Therefore, the smaller integer representing the length of one side is 24, and the consecutive integer representing the length of the other side is 24 + 1 = 25.
Hence, the lengths of the other two sides of the right triangle are 24m and 25m, respectively.
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Write an expression to represent:
5 times the sum of x and 3
Answer:
5(x + 3)
Step-by-step explanation:
the sum of x and 3 is x + 3, then multiply by 5 to obtain
5(x + 3)
Match each function on the left to all points on the right that would be located on the graph of the function. Help!! thanks
Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;
f(x) = 2x + 2 ⇒ (0, 2).
f(x) = 2x² - 2 ⇒ (-1, 0).
\(f(x) = 2\sqrt{x+1}\) ⇒ (0, 2).
What is a function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;
For the ordered pair (0, 2), we have:
f(x) = 2x + 2
2 = 2(0) + 2
2 = 2 (True).
For the ordered pair (-1, 0), we have:
f(x) = 2x² - 2
0 = 2(-1)² - 2
0 = 2 - 2
0 = 0 (True).
For the ordered pair (0, 2), we have:
\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)
2 = 2 (True).
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Estimate the difference.
689.2 - 263 = ?
To estimate the difference, first round each number to the nearest hundred.
PLZ HELP ME I AM STUCK ON THIS QUESTION :(
Answer:430.2
Step-by-step explanation:
Find the value of x .. assume that segments that appear to be tangent are tangent .
We got x = 16.54 by using Pythagorean theorem .
What is the Pythagorean theorem in plain English?
According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.angle of semicircle is always be 90° .
18² = 7.1² + x²
324 = 50.41 + x²
x² = 324 - 50.41
= 273.59
x = √ 273.59
x = 16.54
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Limit of f(t) as t approaches 0. f(t) = (t sin(t)) ÷ (1-cos(t))
Recall the Pythagorean identity,
\(1-\cos^2t=\sin^2t\)
To get this expression in the fraction, multiply the numerator and denominator by \(1+\cos t\):
\(\dfrac{t\sin t}{1-\cos t}\cdot\dfrac{1+\cos t}{1+\cos t}=\dfrac{t\sin t(1+\cos t)}{\sin^2t}=\dfrac{t(1+\cos t)}{\sin t}\)
Now,
\(\displaystyle\lim_{t\to0}\frac{t\sin t}{1-\cos t}=\lim_{t\to0}\frac t{\sin t}\cdot\lim_{t\to0}(1+\cos t)\)
The first limit is well-known and equal to 1, leaving us with
\(\displaystyle\lim_{t\to0}(1+\cos t)=1+\cos0=\boxed{2}\)
Draw the net and calculate the surface area .
Hello!
surface area
= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)
= 160cm²
Help help help help help
Answer:
500
Step-by-step explanation:
65 is 13% of 500
500 x .13= 65
Please help me answer the question from the photo
Answer:
A
Step-by-step explanation:
as it is a reflection (as in a mirror or in a lake, or ...), the distances from either side of the mirror must be equal.
I need help please help me with this
Answer:
120
Step-by-step explanation:
MNT is equal to RQT.
That means R equal to M, T equal to T, equal to N.
Q also equals 180-(T+R)
Q=180-(35+25)
Q=180-60
Q=120
Number of Computers
72
60
48
36
24
12
V
1 2 3 4 5 6 7 8 9 10 11 12
Number of Days
The graph shows a proportional relationship between
the number of computers produced at a factory per day.
In three days, 36 computers are produced; 48
computers are produced in 4 days; and 60 computers
are produced in 5 days.
Find the unit rate of computers per day using the graph.
Unit rate:
computers per day
The unit rate of computers per day using the graph is that 12 computers are made per day.
What is a unit rate?The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.
How to find the unit rate of computers per dayTo obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x
So, it is given by:
\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)
\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)
\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)
\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)
\(\bold{Slope = 12}\)
Unit rate = 12 computers per day.
The attachment of the graph is given below.
Therefore, the unit rate of computers per day is 12.
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Which of the following are possible measures for the angle shown? Select all that apply.
Answer:
-510 degrees and -210 degrees :)
Step-by-step explanation:
An angle is a figure created by two rays. The measure of the angle can be written as 150° or -210°.
What is an angle?An angle is a figure created by two rays, known as the sides of the angle, that have a common terminus, known as the vertex of the angle. Angles created by two rays lie in the plane containing the beams.
The measure of the angle measured from the positive x-axis in an anticlockwise direction will be,
\(\theta = 180^o-30^o = 150^o\\\\\)
The measure of the angle measured from the positive x-axis in clockwise direction will be,
\(\theta = 180^o+30^o = -210^o\)
Hence, the measure of the angle can be written as 150° or -210°.
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Show how you arrived at your solution on the answer sheet for full credit. Write neatly, clearly and be organized.
11. A maker of frozen meals claims that the average caloric content of its meals is 800. A
researcher tested 12 meals and found that a sample mean was 815 calories and the sample
standard deviation 25. Is there enough evidence to reject the claim at a =0.02? Assume the
variable is normally distributed. Use p-value method or traditional method. (hint: two-tail
test) write your answer three decimal places (8 points)
Step-by-step explanation:
A car is on a slope of 10degree above the horizontal . a force 1000N is applied to the car up the line of the slope. the car has amass of 500 kg . what is the acceleration of the car
Compute the loss of head and pressure drop in 200 ft of horizontal 6-in diameter asphalted cast iron pipe carrying water with a mean velocity of 6 ft/s. For water: rho = 1.94 slug/ft3 and μ = 2.09x10-5 slug/ft-s (ν = μ/rho). Assume ε = 0.0004 ft.
Answer:
The answer is below
Step-by-step explanation:
12 inches = 1 ft.
6 inches = 6 inches * (1 ft./12 inches) = 0.5 ft.
Therefore the diameter of the cast iron (D) = 6 inches = 0.5 ft.
The area of cast iron (A) = πD²/4 = π(0.5)²/4 = 0.196 ft²
The velocity (V) = 6 ft./s, the acceleration due to gravity (g) = 32.2 ft./s²
ε/D = 0.0004 ft./ 0.5 ft. = 0.0008
Using the moody chart, find the line ε/D = 0.0008 and determine the point of intersection with the vertical line R = 2.7 * 10⁵. Hence we get f = 0.02.
The head loss (h) is:
\(h_f=f*\frac{L}{d}* \frac{V^2}{2g}=0.02*\frac{200\ ft}{0.5\ ft} *\frac{(6\ ft/s)^2}{2*32.2\ ft/s^2}=4.5\ ft\)
The pressure drop (Δp) is:
Δp = ρg\(h_f\) = \((62.4\ lbf/ft^3)(4.5\ ft)= 280\ lbf/ft^2\)
G measures 117, angle c measures 22, and angle e measures 40. Angle f
Je suis américain et habite dans les montagnes vertes du vermont . Je premier apprend français il y a un an parce que c'est un beau langue . Oui, je sais mon français est mauvais, mais J'aime l'apprendre . Je suis dix-sept et j'ai un chien blanc petit . Ma famille l'appelle snowball et il est tres gentil . Mon préféré endroit en la monde est les montagnes car ils sont très beau dans tout quatre saisons . Merci pour votre temps et au revoir .
Boris started on the treadmill after setting timer for 99 minutes. The display says he have finished 43% of his run. How many minutes have gone by. Round to the nearest tenth
318÷53 with a remainder
Answer:
6
Step-by-step explanation:
318 / 53 = 6
the remainder is 0
(9.42x10^4)(6.45x10^2)
Simplify using a scientific calculator.
Write each answer in scientific notation.
Sone help me understand how to do this
60.759×10⁶ is the value of the expression (9.42×10⁴)(6.45×10²).
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (9.42×10⁴)(6.45×10²)
We have to find the value of the expression.
9.42×6.45×10²×10⁴
60.759×10²×10⁴
Bases are same then the powers will be added.
60.759×10⁶
Hence, 60.759×10⁶ is the value of the expression (9.42×10⁴)(6.45×10²).
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What formula do I use for this? How do I get the points to graph?
The graph of the function y = 5|x - 4| is added as an attachment
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
y = 5|x - 4|
The above function is an absolute value function that has been transformed as follows
Vertically stretched by a factor of 5Shifted right by 4 unitsNext, we plot the graph using a graphing tool by taking not of the above transformations rules
The graph of the function is added as an attachment
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