[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{7 \dfrac{2}{3} + \dfrac{4}{7}}[/tex]
[tex]\huge\textbf{Solving:}[/tex]
[tex]\mathbf{7 \dfrac{2}{3} + \dfrac{4}{7}}[/tex]
[tex]\mathbf{= \dfrac{7\times3+2}{3} + \dfrac{4}{7}}[/tex]
[tex]\mathbf{= \dfrac{21 + 2}{3} + \dfrac{4}{7}}[/tex]
[tex]\mathbf{= \dfrac{23}{3} + \dfrac{4}{7}}[/tex]
[tex]\mathbf{= \dfrac{173}{21}}[/tex]
[tex]\mathbf{\approx 8 \dfrac{5}{21}}[/tex]
[tex]\huge\textbf{Answer:}[/tex]
[tex]\huge\boxed{\mathsf{8 \dfrac{5}{21}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
[tex]8\frac{5}{21}[/tex]
Step-by-step explanation:
[tex]7\frac{2}{3} +\frac{4}{7} = 7\frac{14}{21} +\frac{12}{21} = 8\frac{5}{21}[/tex]
What is the value of log(x exponent 2 y exponent 3 divided by z) when given the following:
log(x) = 3
log(y) = 2
log(z) = -1
A. 12
B. 13
C. 16
D. 18
Urgently need answer
Answer:
B. 13
Explanation:
[tex]\sf\:Given\:expression: log(\dfrac{x^2 y^3}{z} )[/tex]
Logarithm rules:
[tex]\sf (i) \ \sf log(ab) = log(a) + log(b)\\ \\ (ii) \ log(a/b) = log(a) - log(b)\\\\ (iii) \ log(a^n) = n log(a)[/tex]
Breakdown of the expression:
[tex]\rightarrow \sf log\left(\dfrac{x^2y^3}{z}\right)[/tex]
[tex]\rightarrow \sf log\left(x^2\right) + log\left(y^3\right) - log(z)[/tex]
[tex]\rightarrow \sf 2\log\left(x\right)+3\log \left(y\right)-\log \left(z\right)[/tex]
insert given values
[tex]\rightarrow \sf 2(3)+3(2)-(-1)[/tex]
[tex]\rightarrow \sf 13[/tex]
In the video Mouse Count, Miss Ashley read a book about a snake that captured mice and placed them one-by- one in a jar for his dinner. Which Number and Operations standard would this part of the story represent?
A. Combining sets
B. Removing sets
C. Dividing into equal parts
Based on the fact that the snake was placing the mice one - by - one into a jar, this is A. Combining sets.
What does combining sets entail?When sets are combined, it means that numbers from a certain set of variables are combined with those from another set.
The snake had captured the mice separately which means they were in different sets. Putting them into one jar means they are being combined so this is combining sets.
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LMNP is rotated 180 degrees clockwise around the origin. What are the coordinates of L?
[tex]\huge\boxed{L^\prime(0, -1)}[/tex]
To rotate a point around the origin by 180 degrees, multiply both parts of the coordinate point by [tex]-1[/tex]. (This means you go from [tex](x, y)[/tex] to [tex](-x, -y)[/tex].)
[tex]L(0, 1)[/tex]
[tex]L^\prime(0*(-1), 1*(-1))\\\boxed{L^\prime(0, -1)}[/tex]
SEVEN TIMES THE SUM OF THREE CONSECUTIVE EVEN INTEGERS IS 140 MORE THAN ELEVEN TIMES THE
MIDDLE INTEGER. FIND THE INTEGERS
The integers are 12,14 and 16
How to determine the integers?Consecutive even integers are represented as:
x, x + 2 and x + 4
So, the statement is represented as:
7 * (x + x + 2 + x +4) = 140 + 11 * (x + 2)
Evaluate the like terms
7 * (3x + 6) = 140 + 11 * (x + 2)
Open the brackets
21x + 42 = 140 + 11x + 22
Collect the like terms
21x -11x =
Evaluate
10x = 120
Divide by 10
x = 12
So, we have
x + 2 = 14
x + 4 = 16
Hence, the integers are 12,14 and 16
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find domain and range
Domain: [-4, ∞)
Range: (-∞, 0]
*Domain are all x-values listed. Here you can see the graph going the right (positive) of -4 (Doesn't go to the left)
*Range are all y-values listed. Here you can see the graph starts from zero and goes down (negative)
Hope it helps!
What the 29th square number?
Answer: 841
Step-by-step explanation:
29×29=841
Use the demoivres theorem
By de Moivre's theorem,
[tex]\left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)^{18} = \cos\left(\dfrac{18\pi}6\right) + i \sin\left(\dfrac{18\pi}6\right) \\\\ ~~~~~~~~ = \cos(3\pi) + i \sin(3\pi) = \boxed{-1}[/tex]
The value of the given complex number is -1
De'moivres theorem
Given the polar form of a complex number expressed as:
[tex](cos\theta + isin\theta)^n\\[/tex]
This can also be expressed according to the de moivre's theorem as;
[tex]=(cos\theta + isin\theta)^n\\\\=(cosn\theta+isinn\theta)[/tex]
Given the expression below;
[tex](cos\frac{\pi}{6} + isin\frac{\pi}{6} )^{18}\\(cos18\cdot\frac{\pi}{6} + isin18\cdot\frac{\pi}{6} )\\(cos3\pi + isin3\pi)\\=-1[/tex]
Hence the value of the given complex number is -1
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Which is the distance betweeen parallel lines with the equations y=-1/3x+3 and y=-1/3x-7
Answer:
the distance is 10
Step-by-step explanation:
since the slope is the same you know they're parallel, but just find the difference from the two y intercepts (the +3/-7) the difference is 10, so 10.
Miss Brandy is preparing her unit on architecture. She set up the construction area with a variety of objects and tools for measuring. She also included paper and pencils for children to record their results. An assortment of books on architecture were set up for the children to explore. Which mathematical thinking standard is being addressed in this learning center?
A. Children are extending a simple AB repeating pattern.
B. Children are identifying measurable attributes such as length and weight and solve problems by making direct comparisons of objects.
C. Children are constructing and count sets of objects.
In this scenario, children are identifying measurable attributes such as length and weight and solve problems by making direct comparisons of objects.
What is measurement?Measurement refers to a process through which the dimensions, size (weight), or other physical quantities of magnitude that are associated with an object is taken, especially for use in a scientific research and experiment such as direct comparison.
In this scenario, we can infer and logically deduce that the children are identifying measurable attributes such as length and weight and solve problems by making direct comparisons of objects.
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7. Write a general formula to describe the variation: x varies directly with the cube of y; x = 8 when y = -8.
Answer: it should be this M=kb^3/B^2
Step-by-step explanation:
Compare the graph of m(x) = 0.7x² + 4 with the graph of n(x) = x².
The graph of m(x) is narrower.
Both graphs open upward.
Both have the axis of symmetry x = 1.
The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).
The graph of m(x) is wider.
Both graphs open upward.
Both have the axis of symmetry x = 0.
The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).
The graph of m(x) is wider.
Both graphs open downward.
Both have the axis of symmetry x = 0.
The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).
The graph of m(x) is narrower.
Both graphs open upward.
Both have the axis of symmetry x = 1.
The vertex of m(x) is (0, 4), the vertex of n(x) is (0, 2).
Answer:
B.) The graph of m(x) is wider.
Both graphs open upward.
Both have the axis of symmetry x = 0.
The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).
Step-by-step explanation:
When the coefficient before x² is greater than 1, the curve of the graph is narrower. When the coefficient is less than 1, the curve of the graph is wider.
When the coefficient in front of x² is positive, the graph opens upwards. When the coefficient is negative, the graph opens downwards.
The axis of symmetry is the "x" value which divides the curve into two equal sections. Their axis of symmetry are both x = 0 because their vertexes (the lowest point of the curve) are both at x = 0.
The vertex can be found by plugging x = 0 into both of the equations and then solving. The resulting value is the "y" position of the vertex.
m(0) = 0.7(0)² + 4 n(0) = (0)²
m(0) = 0 + 4 n(0) = 0
m(0) = 4
Therefore, the vertexes are m(x) = (0,4) and n(x) = (0,0).
Answer:
Step-by-step explanation:
m(x) =.7x^2 + 4
n(x) = x^2
In the graph below
green = m(x)
blue = n(x)
Answer:
Just look at the graph belowBoth graphs open upward.The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).The graph of m(x) is wider.Given the right triangle shown, solve for X, Y and Z. The triangle may not be drawn to scale
Answer:
X ≈ 8.58 ftY ≈ 9.46 ftZ = 65°Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to help you remember the relationships between sides of a right triangle and trig functions of the acute angles. It tells you ...
Sin = Opposite/HypotenuseCos = Adjacent/HypotenuseTan = Opposite/AdjacentSidesThe given triangle shows values of an acute angle and its opposite side. You are to find the other two sides in the triangle, as well as the other acute angle.
X is the side adjacent to the given angle, so the relevant trig relation is ...
Tan = Opposite/Adjacent
tan(25°) = (4 ft)/X
Solving for X gives ...
X = (4 ft)/tan(25°) . . . . . . . . multiply by X/tan(25°)
X ≈ 8.58 ft
Y is the hypotenuse, so the relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(25°) = (4 ft)/Y
Y = (4 ft)/sin(25°) . . . . . . multiply by Y/sin(25°)
Y ≈ 9.46 ft
AngleThe sum of angles in a triangle is 180°, so if one of them is 90°, the sum of the other two is 90°.
Z = 90° -25°
Z = 65°
Pls help! 20 points very ugrent
Answer: -2, 1, all real numbers, all real numbers
Step-by-step explanation:
g o f(n) is basically g(f(n))
Using the question as an example we can get that f(0) = 1 so
g(f(0)) = g(1) = -2
f(1) = 0 so g(f(1)) = g(0) = 1
The domain of f(x) is all real numbers and the range of g(x) is all real numbers
At a party there is one bottle of coke for every 3 guests, one bottle of sprite for every 6 guests, and one bottle of lift for every 4 guests. There are 54 bottles of drink at the party. How many guests are there? At a party there is one bottle of coke for every 3 guests , one bottle of sprite for every 6 guests , and one bottle of lift for every 4 guests . There are 54 bottles of drink at the party . How many guests are there ?
Answer:
72 guests
Step-by-step explanation:
We can add up the numbers of bottles per guest, then use that total to find the number of guests from the number of bottles.
SetupLet g represent the number of guests at the party. Then there are ...
g/3 bottles of cokeg/6 bottles of spriteg/4 bottles of liftThe total number of bottles is ...
g(1/3 +1/6 +1/4) = 54
SolutionMultiplying by the inverse of the coefficient of g, we find its value to be ...
g(4/12 +2/12 +3/12) = g(9/12) = 54
g = 54(12/9) = 72
There are 72 guests at the party.
Drag each graph to the correct location on the table. The points on the graphs represent relations. Classify these relations according to whether or not they are functio 1-3 -2 -1 3. -40 2 1 -2 -3 1 2 Function -3 -2 -1 -1 -2 3 D 2 3 -3 2 101 -1 3 1240 1 24 2 10 3 Not a Function Drag each graph to the correct location on the table . The points on the graphs represent relations . Classify these relations according to whether or not they are functio 1-3 -2 -1 3. -40 2 1 -2 -3 1 2 Function -3 -2 -1 -1 -2 3 D 2 3 -3 2 101 -1 3 1240 1 24 2 10 3 Not a Function
Answer:
Function: BNot a function: A, CStep-by-step explanation:
A relation is a function if there is only one y-value for each x-value. If you can draw a vertical line on the graph that intersect more than one point, the relation is not a function. (This is the "vertical line test.")
ApplicationGraph A: there are 3 y-values associated with x=2. Not a function.
Graph B: passes the vertical line test: A function.
Graph C: there are 2 y-values at each of x=1 and x=2. Not a function.
Helppppppo points to give
a) The point (2, -7/5) is not a point on the graph?
b) The value of f(x) when x is 1 is -1/3 and the point on the graph is (1, -1/3)
c) The value of x for f(x) = 2 is 22 and the point on the graph is (22, 2)
d) The domain of x is all real values of x ≠ 10
e) The x intercept is -2
f) The y intercept is -1/5
What is a Function?Function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output and not one input for two outputs.
Analysis:
a) To test if the point (2, -7/5) is a point on the graph, we put in x = 2 into the function,
f(2) = 2+2/2-10 = 4/-8 = -1/2 ≠ -7/5. Therefore (2, -7/5) is not a point on the graph.
b) if x = 1, f(1) = 1 +2 / 1-10 = 3/-9 = - 1/3
The point on the graph is (1, -1/3)
c) if f(x) = 2, then 2 = x+2/x-10
2(x-10) = x+2
2x -20 = x+2
2x-x = 2+20
x = 22, the point on the graph is (22, 2)
d) The domain of the function is such that the denominator would not be zero.
so if x - 10 ≠ 0
Then the values of x ≠ 10 are the domain of the function.
e) The x intercept of the graph is the point at which f(x) = 0
0 = x+2/x-10
x+2 = 0
x = -2. The x-intercept is -2.
f) the y-intercept is such that x = 0
0+2/0-10 = 2/-10 = -1/5
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84. A poll done for Newsweek found that 13% of Americans have seen or sensed the presence of an angel. A contingent doubts that the percent is really that high. It conducts its own survey. Out of 76 Americans surveyed, only two had seen or sensed the presence of an angel. As a result of the contingent’s survey, would you agree with the Newsweek poll? In complete sentences, also give three reasons why the two polls might give different results.
Critical value z_{0.05}=-1.645
Decision Rule, Reject H if z< -1.645
We do not reject the null hypothesis.
What is the Decision?Generally, the equation for the hypothesis is mathematically given as
H P=0.3
H2:P<0.13
Therefore
[tex]z=\frac{p'-p}{\sqrt{\frac{p(1-p)}{n}}}\\\\\\z=\frac{0.11-0.13 }{\sqrt{\frac{0.13(1-0.13)}{76}}}[/tex]
z=-0.52
In conclusion, from the table
Critical value z_{0.05}=-1.645
Decision Rule, Reject H if z< -1.645
In conclusion, we do not reject the null hypothesis.
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Which of the following is the best buy?
a 6 oz box of rice for $0.90
a 12 oz box of rice for $1.93
a 16 oz bag of rice for $2.42
a 9 oz box of rice $1.25
The $1.25 one for 9 Oz box of rice would be the best buy.
How to find the Unit Price?To get the best buy among the given items and prices, we need to find the unit price. Thus, the formula is;
Unit price = Price/Quantity
A) Unit Price = 0.90/6 = 0.15
B) Unit Price = 1.93/12 = 0.15083
C) Unit price = 2.42/16
Unit Price = 0.15125
D) Unit Price = 1.25/9 = 0.138
The $1.25 one for 9 Oz box of rice would be the best buy.
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PLEASE ANSWER
Consider the data set displayed on the following box plot.
Which of the following statements about the data set are true? Select all that apply.
A.The interquartile range is 10.
B.There is one outlier.
C.There are no outliers.
D.The data is skewed.
E.The interquartile range is 8.
F.There are two outliers
G.The data is symmetric.
The true statements are:
The interquartile range is 10.
The data is skewed.
What are the true statements?A box plot is used to study the distribution and level of a set of scores
The end of the first whisker represents the minimum number and the end of the second whisker represents the maximum number.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. The interquartile range is the difference between the first and third quartile.
Interquartile range = 9 - (-1) = 10
A box plot is negative skewed because the median is not at the center of the box.
An outlier would be within: (Q1 - 1.5 * IQR or Q3 + 1.5 * IQR).
- 1 - (1.5 x 10 ) = -16
9 + (1.5 x 10) = 24
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1/2 divided 8 as a whole number
Answer:
16
Step-by-step explanation:
A fraction that is divided by a number is just multiplication with the denominator. So with that 8(2)=16
The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an elephant weighs 3200 pounds on Planet A, find the
elephant's weight on Planet B.
The elephant's weight on Planet B is….. lb.
A ratio shows us the number of times a number contains another number. The elephant's weight on Planet B is 96 pounds.
What is a Ratio?A ratio shows us the number of times a number contains another number.
The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3.
Weight on Planet A/ Weight on planet B = 100 / 3
Now, the weight of the elephant on planet A to Planet B will be,
elephant's weight on Planet A/elephant's weight on Planet B = 100 / 3
elephant's weight on Planet B = (3 ×3200)/100
elephant's weight on Planet B = 96 pounds
Hence, the elephant's weight on Planet B is 96 pounds.
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6(1+5x)=5(1+6x) solve x
Answer:
No solutions
Step-by-step explanation:
Hello!
To solve for x, we should expand the parenthesis and isolate the variable x.
Solve for x6(1 + 5x) = 5(1 + 6x)6 + 30x = 5 + 30x6 ≠ 5The are no solutions for x, as 6 does not equal to 5.
write an inequality to represent the graph
Answer:
y ≤ 2.5x-3
Step-by-step explanation:
we know two points: (2 , 2 ) and ( 0 , -3)
[tex]Grad = \frac{2--3}{2-0} =\frac{5}{2} =2.5\\[/tex]
we also know the y intercept is -3
therefore equation in question is : [tex]y = 2.5x-3[/tex]
we take any point either above the line or below the line and substitute in the equation above. Let us try point (0,0) which is above the line and in the unwanted(shaded region):
y = 2.5x-3
0=2.5(0)-3
0=-3
Normally 0 can never be equal to -3 but is ≥ -3.
Since the point taken was not in the wanted region we reverse ≥ to ≤ to show the wanted region. The inequality in question becomes :
y ≤ 2.5x-3
write as an algebraic expression and then simplify the number that is x more than 2x+1
The algebraic expression is x > 2x + 1 and simplification form of the algebric expression is x < -1
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
The number that is x more than 2x+1
x is the number.
x > 2x + 1
After simplification:
2x - x < -1
x < -1
x ∈ (-∞, -1)
Thus, the algebraic expression is x > 2x + 1 and simplification form of the algebric expression is x < -1
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Peter received a $15 tip on a meal that cost $130. What percent of the meal cost was the tip?
11.5%
21%
18.5%
14%
Pls Help! Geometry
How much will the molding cost?
Answer: $412.50
Step-by-step explanation:
The area of the square formed by combining the painting and the molding is [tex](25)(28)=700[/tex] square inches.
The area of the painting itself is [tex](22)(25)=550[/tex] square inches.
Therefore, the area of the molding is [tex]700-550=150[/tex] square inches, and thus costs [tex](150)(2.75)=\$412.50[/tex]
Write an equation of the line passing through the point (7,3) that is parallel to the line y=2x-4.
Answer:
y=2x-11
Step-by-step explanation:
arralel lines have same gradient
since gradient of the known line is 2( the coefficient of x), it therefore follows that the gradient of the second line we want to find is also 2
So we know the gradient of the second line is 2, and we have one known point (7,3). We can therefore apply the formula for finding gradient to come up with the line
[tex]2=\frac{y-3}{x-7} \\\\y-3=2(x-7)\\\\y-3=2x-14\\\\y=2x-14+3\\\\y=2x-11[/tex]
you have 32 tbsp of peppercorns you need 2 teaspoons to make one serving of cajun seasoning how many servings can u make
Answer:
48 servings
Step-by-step explanation:
3tsp=tbsp
32*3=96
96/2=48
What is the range of the function y=3√x+8?
-∞xy<∞
-8
0≤y<∞
2≤y<∞
The range of the function the as given in the equation is; -∞ ≤ y < ∞.
What is the range of the function?It follows from the task content that the function given is; y=3√x+8.
On this note, it follows that the range of the function is the set of all possible outputs, y values and in this case is; -∞ ≤ y < ∞.
It therefore follows that the range of the function is as indicated above as all X-values (domain) must be positive and the square root of x yields a positive or negative real number.
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Someone help me with this please, solve it in process please ;-;
Step-by-step explanation:
2A and 2B are scalar multiplications : every item in the matrix has to be multiplied by that factor.
the subtraction then of 2A - 2B is simply to subtract every positive in B from the corresponding same position in A.
that is all.
2A =
4 0
-6 2
2B =
0 2
-4 6
2A - 2B =
4-0 0-2
-6--4 2-6
=
4 -2
-2 -4