There are 3 tens in 7x30 or 30x7.
What is an equation?
A mathematical statement is referred to as an equation when two expressions are connected by the equal sign. A mathematical equation serves as the connection between two expressions on each side of the sign. Usually, there is only one variable and an equal sign.
Equations can be categorized as identities or conditional equations. An identity holds true regardless of the value given to the variables. A conditional equation's variables can only have specific values that produce the truth.
An equation is created by joining two expressions with an equal sign. The solution to an equation is a number that may be used as the variable to generate a true number statement.
Here, we have
7x30 = 7 x 10 x 10 x 10
The value of 7x30 = 210
Hence, there are 3 tens in 7x30 or 30x7.
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Use the given measurements to solve the triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.
a=400, b=300
[tex]\frac{\sin \theta}{300}=\frac{\sin 2\theta}{400} \\ \\ \frac{\sin \theta}{300}=\frac{2\sin \theta \cos \theta}{400} \\ \\ \frac{1}{300}=\frac{\cos \theta}{200} \\ \\ \cos \theta=\frac{2}{3} \\ \\ \theta=\arccos(2/3) \\ \\ \theta \approx \boxed{48^{\circ}}[/tex]
Five thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $700, 3 prizes of $100, 5 prizes of $10, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket?
This raffle's expected value per ticket is $ 0.25.
Given that 5,000 tickets are sold at $1 apiece for a charity raffle, and tickets are to be picked at random, the following monetary prizes will be awarded.
To estimate the expected value of this raffle if you buy 1 ticket, apply the following calculation: 1 prize of $ 500, 3 prizes of $ 200, 5 prizes of $ 10, and 20 prizes of $ 5.
⇒ (500 + 3 x 200 + 5 x 10 + 20 x 5) / 5000 = X
⇒ (500 + 600 + 50 + 100) / 5000 = X
⇒ 1250/5000 = X
Apply the division operation, and we get
⇒ 0.25 = X
Therefore, this raffle's expected value per ticket is $ 0.25.
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What is the area of the polygon below?
A. 147 square units
B. 111 square units
C. 120 square units
D. 156 square units
Answer:
A. 147
Step-by-step explanation:
Divide the polygon into rectangles.
You will have 2 rectangles:
1) 3 x 10
2) 9 x 13
Now you just need to find the area of this 2 rectangles and add them up.
Find the equivalent measure.
19 qt L
Click the icon to view the customary and metric unit equivalents.
-
19 qtL
(Type an integer or decimal rounded to the nearest tenth as needed.)
The equivalent measure of 19 quarts is either 608 fluid ounces or 18.094 liters.
What is the equivalent measure?
In mathematics, and more specifically in measure theory, equivalence refers to the idea that two measures are qualitatively similar. The two measures specifically agree on which events have measure zero.
The unit "qt" stands for quart, which is a unit of volume.
It is equal to 32 fluid ounces or 0.946 liters.
Therefore, 19 quarts is equal to 19 * 32 = 1932= 608 fluid ounces,
or 19 * 0.946 = 190.946 =18.094 liters.
Hence, the equivalent measure of 19 quarts is either 608 fluid ounces or 18.094 liters.
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PLEASE best explanation gets brainliest
Answer:
55
Step-by-step explanation:
Because you would minus 180-125 to get angle 1 and they said that angle 2 is parallel so they would be the same anwser so the answer is 55.
Lucas is 5 inches taller than Tamika, and the sum of their heights is 137 inches?
Answer:
Lucas 71 inches
Tamika 66 inches
Three varieties of coffee Coffee A, Coffee B, and Coffee C are combined and roasted, yielding a 55-lb batch of coffee beans. Twice as many pounds of Coffee C, which retails for $10.39 per lb, are needed as Coffee A, which sells for $14.99 per lb. Coffee B retails for $13.99 per lb. How many pounds of each coffee should be used in a blend that sells for $12.61 per lb?
Coffee A is 12.241 pounds, Coffee B is 18.269 pounds and Coffee C is 24.482 pounds.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Let a pounds of coffee A needed
Let b pounds of coffee B needed
Let c pounds of coffee C needed
c= 2a.................(1)
a+ b+c= 55..........(2)
and, 14.99 a+ 13.99 b + 10.39 c /55 = 12.61
1499a + 1399 b + 1039 c = 69,355...............(3)
Subtract (2) from (3), we get
1499 a+ 1399 b + 1039 c= 69355
- 1039 a - 1039 b - 1039 c = 57145
_____________________________
460 a + 360 b = 12210
46a+ 36 b = 1221
b= 1221/ 36 - 46 a/ 36
b= 407 / 12 - 23 a / 18
Put b in Equation (2)
a + 407 / 12 - 23 a / 18 + 2a= 55
-5a / 18 + 2a + 407/ 12 = 55
31a/ 18 = 253/ 12
a= 4554 / 372
a = 2277/ 186
a= 759/ 62
a= 12.241
and, c=2a = 24.482
b= 33.91 - 15.641
b= 18.269
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If two balls with different speeds roll off the edge of a table at the same time, which one hits the floor first, the faster or the slower ball? Why or why not?
Both balls will strike the ground simultaneously, but the faster ball will do so farther away from the table.
What is acceleration due to gravity ?The unit g stands for gravitational acceleration. At sea level, the standard value of g on earth's surface is 9.8 m/[tex]s^{2}[/tex]
They will strike the ground simultaneously if the table and the ground are both flat.
It is customary to divide an object's motion into a vertical component and a horizontal component. While they are on the table, neither of the balls is moving vertically. Both balls begin to accelerate downward as soon as they leave the table due to the effects of gravity. Given that both balls experience the same acceleration from gravity, they will fall at the same rate and with the same downward velocity.
Both balls will strike the ground simultaneously, but the faster ball will do so farther away from the table.
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Find the direction of the sum of these two vectors:
By using the concept of vector, it can be calculated that
Direction of the sum is 10.87° below the horizontal.
What is vector?
Anything that has both magnitude and direction and follow the vector addition law is called vector.
A = 2.71 m
[tex]A_x = 2.71 cos 60 = 1.355 \ m\\A_y = -2.71 sin 60 = -2.35 \ m[/tex]
B = 3.14 m
[tex]B_x = 3.14 cos 30 = 2.71 \ m\\B_y = 3.14 sin 30 = 1.57 \ m[/tex]
Sum of A and B = (1.355 +2.71) i + (-2.35 + 1.57) j
= 4.065i - 0.78j
Let the angle be [tex]\theta[/tex]
[tex]tan\theta = \frac{0.78}{4.065}\\tan\theta = 0.192\\\theta = tan^{-1}(0.192)\\\theta = 10.87^{\circ}[/tex]
Direction of the sum is 10.87° below the horizontal.
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The graph shows a translation of the function f(x) = |x|. What absolute value function is represented by the graph?
A V shape with vertex at negative 1 point 5 comma zero and passing through the points negative 2 comma 1 and negative 1 comma 1.
A. f(x) = |x| + 1.5
B. f(x) = |x| − 1.5
C. f(x) = |x − 1.5|
D. f(x) = |x + 1.5|
The absolute value function that is represented in the graph is f(x) = |x + 1.5| So the correct option is D.
What absolute value function is represented by the graph?The general absolute value function is:f(x) = |x|This absolute value function has a vertex at the point (0, 0). We know that the graphed function has a vertex at the point (-1.5, 0).
So basically we had a horizontal translation of -1.5 units or 1.5 units to the left. That is written as: g(x) = f(x + 1.5)
Replacing the absolute value function we get:g(x) = |x + 1.5|
Then the correct option is D.
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a line with a slope of -3 passes through the point -3,8 what is its equation in slope intercept form
Expand the log completely
Answer:
log(2)√xy
________
y
there good luck
Sam and Liam raced up and then back down a hill. Sam's average speed up the hill
was 1 mph, and his average speed down the hill was 9 mph. Liam ran up the hill
and down the hill at 2 mph. If the trail from the bottom to the top of the hill is 1
mile long, how much time did it take each boy to finish? Who was the winner?
Using the speed formula, we know that Liam finished in 1 hour as opposed to Sam's 1/ 19 hours, earning him the victory.
What is speed?Speed is calculated as follows: speed = distance * time.
Knowing the units for distance and time is necessary to calculate the units for speed.
The units will be in meters per second (m/s) in this example since the distance is measured in meters (m) and the time is measured in seconds (s).
So, the speed formula is:
Speed = Distance/Time
Taking time for the subject:
Time = distance/Speed
Now, Sam:
Time spent ascending the hill = 1/1 = 1 hour
Time spent descending the hill = 1/9 hours
Sam spent 1 1/the9 total minutes climbing and descending the hill.
Now, Lian:
Time spent ascending the hill = 1/2 hours
Time spent descending the hill = 1/2 hour
Total time spent ascending and descending the hill = 1/2 + 1/2 = 1 hour
Sam, therefore, took 1/9 hour longer than Liam.
Therefore, using the speed formula, we know that Liam finished in 1 hour as opposed to Sam's 1/ 19 hours, earning him victory.
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Consider the simultaneous equations
3x² + 2xy = 4
x + y = a
where a is a real constant.
Find the complete set of values of a for which the equations have two distinct real solutions for x.
There are no values of a.
-2 < a < 2
-1 < a < 1
a = 0
a < -1 or a < 1
a < -2 or a < 2
All real values of a
The correct option is All real values of a.
What is the real number?
The positive and negative integers, as well as the fractions created from them (also known as rational numbers), as well as the irrational numbers, are all real numbers.
We have,
3x² + 2xy = 4 ...................(1)
x + y = a ...................(2)
By converting the second equation equals to y:
y = a - x .....................(3)
By substituting the (3)rd equation into (1), we get
3x² + 2xy = 4
3x² + 2x(a - x) = 4
3x² + 2ax - 2x² = 4
x² + 2ax = 4
x² + 2ax - 4 = 0
Discriminant = 4a² + 16 >= 0
2 distinct solutions & is ok for all a.
hence, the correct option is All real values of a.
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multiply 1/2 x 1/4 equals ?
Answer:
1/8 or 0.125
Step-by-step explanation:
1/2×1/8
multiply the numerators 1×1=1 and multiply the denominators 2×4=8
Final answer =1/8 or 0.125
ZA and ZB are vertical angles. If m/A = (6x +29)° and m
LB = (7x+25)°, then find the value of x.
The value of x is 4.
What are vertical angles?
The opposing angles formed when two lines cross. They are constantly on par. In this illustration, the angles a° and b° are vertical. The term "vertical" refers to the vertex, not up or down, where they cross.
Here, we have
Given the following parameters
m∠A= (6x +29)° and
m∠B = (7x+25)°
Now, we equate both angles to find the value of x and we get
6x+29 = 7x + 25
6x-7x = 25 - 29
-x = -4
x = 4
Hence, the value of x is 4.
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By looking at the equation of the least-squares regression line, you can see that the correlation between height and arm span is (a) greater than zero. (b) less than zero. (c) 0.93 . (d) 6.4 (e) Can't tell without seeing the data.
As per the given least square regression line, the correlation between the height and the arm span is (a) greater than zero.
Regression line:
In statistics, regression line refers the an estimate of the line that describes the true, but unknown, linear relationship between the two variables.
Given,
Here we need to find the correlation between the height and the arm span by using the given least square regression line.
Let us consider the following situation,
"Measurements on young children in Mumbai, India, found this least‐ squares line for predicting height (y) from arm span (x): predicted y = 6.4 + 0.93x. Measurements are in centimeters (cm)."
While we looking into this one we have identified that the predicted function y = 6.4 + 0.93x, is defines the value of height.
So, here y is the dependent variable and the x is the independent value.
This means that the value x is smaller comparatively y value.
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what are the cooridinates of the point that is 1/6 of the way from A(14, -1) to B(-4, 23)?
Answer:
(11, 3)
Step-by-step explanation:
You want the point 1/6 of the way from A(14, -1) to B(-4, 23).
Dividing pointThe point P that divides AB into the fractional parts k and (1 -k) is ...
P = (1-k)A +kB
ApplicationFor k = 1/6, the dividing point is ...
P = (5/6)(14, -1) +(1/6)(-4, 23) = (5·14 -4, 5(-1) +23)/6 = (66, 18)/6
P = (11, 3)
The point 1/6 of the way from A to B is (11, 3).
You are investing money at 10.5 percent annual interest, compounded continuously. It will take you ______ years to double your investment.
let's take it from the basic of one dolla!, how long will it take for $1 to become $2, namely double, at 10.5%?
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2\\ P=\textit{original amount deposited}\dotfill & \$1\\ r=rate\to 10.5\%\to \frac{10.5}{100}\dotfill &0.105\\ t=years \end{cases} \\\\\\ 2=1e^{0.105\cdot t} \implies \log_e(2)=\log_e(e^{0.105t})\implies \log_e(2)=0.105t \\\\\\ \ln(2)=0.105t\implies \cfrac{\ln(2)}{0.105}=t\implies 6.6\approx t\qquad \textit{about 6 years and 219 days}[/tex]
Assume that the function [tex]f(x) = ax^{2} + bx + c, a \neq 0[/tex] has two real zeros. Prove that the x-coordinate of the vertex of the graph is the average of the zeros of [tex]f[/tex].
(Hint: Use the Quadratic Formula)
For 3, use the table at the right.
3. Jose has $100 to spend at the pet store. He needs to buy
1 bag of dog food and 2 chew toys. How many catnip toys
can Jose buy? Write equations to show each step.
DATA
Barky's Pet Store
Product
Bag of Dog Food
Tex
Bag of Cat Food
Tex
Chew Toy
Catnip Toy
Cost
$35
$18
$12
39
The number of catnip toys that Jose can buy will be 3 catnip toys. All the steps are described below.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The table is given below.
Product Cost
Bag of Dog Food $35
Bag of Cat Food $18
Chew Toy $12
Catnip Toy $9
In the event that, your numbers are unique, you should simply supplant the qualities you have with the methodology here, and you ought to find an exact solution.
Presently, Emma has $100 to spend at the store. Along these lines, we really want to ascertain the amount she spends on shopping:
$35 + 2 x $12 = $59
In this way, she burned through $59 in the store, so she has left:
$100 - $59 = $41
She has $41 left to spend on something different. How about we check whether she has sufficient means to purchase multiple times catnip toys as bite toys:
Chew toys: 3 x 12 = $36
Catnip toy: 3 x 9 = $27
Furthermore, Emma has $41 left, so she can either purchase multiple times bite toys or multiple times catnip toys, however not the two of them at that point, on the grounds that the all-out would be 63% dollars, and she will be missing $22.
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4 There are between 20 and 50 flags.
They can be shared equally among
2 tents or 4 tents or 5 tents.
How many flags are there?
When there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents. The number of flags will be 40.
How to illustrate the information?From the information, there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents.
It should be noted that this simply means that we should find the highest multiple for 2, 4, and 5 between 20 and 50. This is 40.
Therefore, the number of flags is 40.
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Use the L-shaped composite figure formed by two rectangular prisms to answer the question.
What is the surface area of the composite figure in square inches?
(WILL GIVE BRAINLIEST)
The surface area of the composite figure is calculated as: 640 square inches.
What is the Surface Area of a Rectangular Prism?The surface area of a rectangular prism = 2(w*l + h*l + h*w), where:
l = length w = width h = heightThe composite figure can be decomposed into two rectangular prisms, 1 and 2.
Rectangular prism 1:
l = 10 in.
w = 0.5 ft. = 6 in.
h = 4 + 7 = 11 in.
Surface area = 2*(6*10 + 11*10 + 11*6) = 472 in.²
Rectangular prism 2:
l = 10 in.
w = 0.5 ft. = 6 in.
h = 4 in.
Surface area = 2·(6·10+4·10+4·6) = 248 in.²
The area of the surface where both meet = (l)(w) = (10)(4) = 40 in.²
Therefore:
Surface area of the composite figure = 472 + 248 - 2(40) = 640 in.².
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Please help
Whats
30-19+29+30-29-10=
Answer:
31Step-by-step explanation:
[tex]\tt 30-19+29+30-29-10[/tex]
[tex]\tt 11+29+30-29-10[/tex]
[tex]\tt 40+30-29-10[/tex]
[tex]\tt 70-29-10[/tex]
[tex]\tt 41-10[/tex]
[tex]\tt 31[/tex]
__________________
Hope this helps you!
Have a nice day!
Dwayne has collected data on the number of occupants of cars travelling on the road past his house for the past week. Based on his data, he has constructed a probability model for the number occupants of a randomly-selected car on his street. Which of the following could be his model?
The option that can be the model when Dwayne has collected data on the number of occupants of cars travelling on the road is Table B.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true
Given the information, the probability for a will be illustrated as:
a. = 0.6 + 0.2 + 0.2 + 0.1 + 0.05 = 1.15 > 1
b. = 0.5 + 0.25 + 0.05 + 0.06 + 0.04 = 1
c. 2 + 1 + 0.1 + 0.1 + 0.4 = 3.6 > 1
d. 0.5 + 0.25 + 0.25 + 0.125 + 0.125 = 1.25 > 1
e. 0.5 + 0.2 + 0.1 + 0.05 + 0.05 = 0.9 < 1
The correct option that illustrates this is Table B.
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which inequality is less than the quadratic function with zero -7 and 1 and includes the point (2,27/2) on the boundary?
y<-3/2 x²+9 x+21/2
y<3/2 x²+9 x-21/2
y<-3/2 x²-9 x+21/2
y<3/2 x²-9 x-21/2
The inequality is less than the quadratic function with zero -7 and 1 and includes the point (2,27/2) quadratic function is
y < 3/2 x² + 9 x - 21/2How to show the inequality requiredThe problem seeks the inequality that will be less than the quadratic function with zero -7 and 1 and includes the point (2, 27/2).
Therefore the quadratic function should have zeros at -7 and 1
Substituting the point (2, 27/2) to the quadratic function to check the one that gives the points shows that
3/2 x² + 9 x - 21/2 at x = 2
3/2 * 2² + 9 * 2 - 21/2
= 27/2
Solving for the zeros in the quadratic function 3/2 x² + 9 x - 21/2
shows that the zero are at
x = -7 and
Therefore the inequality that meets the condition is y < 3/2 x² + 9 x - 21/2
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TIME SENSITIVE
(2,6)
x-y=4
(a) write an equation of the line that passes through the point and is parallel to the given line
(b) write an equation of the line that passes through the point and is perpendicular to the given line
Answer:
(a) Equation of parallel line is y = x + 4
(b) Equation of perpendicular line is y = - x + 8
Step-by-step explanation:
Given line is
x - y = 4
Rewrite this as
x - 4 = y
or
y = x - 4
This is the equation of a line in slope intercept form which is generally
y = mx + b
where m is the slope and b the y-intercept
Here m = 1, b = -4
(a) A parallel line will have the same slope but a different y-intercept
So for starters we can write the equation of the parallel line as
y = x + b
Since this passes through (2,6) sub 2 for x and 6 for y to get
6 = 2 + b
==> b = 4
Equation of the line is
y = x + 4
(b) A perpendicular line will have as slope -1/m where m is the slope of the original line
Here m = 1, so -1/m = -1/1 = -1
Equation will be of the form
y = -x + b
Since this also passes through (2,6)
6 = -2 + b
==> b = 6 + 2 = 8
Equation of perpendicular line is
y = -x + 8
The formula for estimating the population variance from the sample involves taking the sum of squared deviations and dividing it by ___
The formula for estimating the population variance from the sample involves taking the sum of squared deviations and dividing it by N - 1
Population variance is a measure of dispersion that determines how far each data point is from the population mean.
On the population, the population variance is calculated. When the number of observations grows, a few data points are chosen to represent the entire population.
The variance calculated on these specific data points is referred to as the sample variance. The population variance can be estimated using the sample variance.
When the population variance is unknown , we estimate the population variance by using sample variance
The formula for estimating the population variance from the sample involves taking the sum of squared deviations and dividing it by N-1
Formula of sample variance = [tex]s^2 = \frac{\sum f_i(x_i - \bar{x})}{N-1}[/tex]
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Graph the polygon with the given vertices and its image after a reflection in the line y = x.
A(6, - 3), B(1, - 2), C(4, 1)
The image of the polygon after a reflection in the line y=x is having vertices at A'(-3, 6), B'(-2, 1) and C'(1, 4) as shown in the diagram attached.
What is a reflection?A reflection is a sort of transformation that creates a new shape by flipping a shape, called the preimage, across a line, called the line of reflection (called the image). You may imagine what would occur if the form were turned over the line to graph a reflection.
A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image).
You can picture what would happen if you flipped the form over the line in order to graph a reflection.
If a point A(x, y) is reflected about the line y = x,
the new point would be at A'(y, x)
Given the polygon with vertices at A(6, -3), B(1, -2) and C(4, 1).
The image of the polygon after a reflection in the line y=x has vertices at:
A'(-3, 6), B'(-2, 1) and C'(1, 4)
The image of the polygon is attached.
Therefore, according to the attached graphic, the vertices of the polygon's image after a reflection in the line y=x are located at A'(-3, 6), B'(-2, 1), and C'(1, 4).
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In a recent poll, 280 people were asked if they liked dogs, and 42% said they did. Find the margin of error of this poll, at the 90% confidence level.
If in a recent poll, 280 people were asked if they liked dogs, and 42% said they did. the margin of error of this poll, at the 90% confidence level is 0.05.
How to find the margin of error?Sample proportion =42%(phat)
Sample size =280
Standard error = √(0.42×( 1- 0.42)/280)
Standard error = √(0.42×(.58)/280)
Standard error =0.029
Hence,
Margin of error = z-critical for 90% confidence level× Standard error
Zα/2 = 1.645 for 90% confidence
Margin of error = 1.645 × 0.029
Margin of error = 0.047
Margin of error =0.05 (Approximately)
Therefore the margin of error is 0.05.
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