About 200 teddy bears in the store.
Given,
The ratio of the number of dolls to the number of teddy bears is 6:5
and, The store has 240 dolls.
To find the number of teddy bears are in the store.
Now, According to the question:
Total no. of dolls are 240
The ratio of dolls and teddy bears are 6:5
Then, For dolls
= 240/6 = 40dolls
So, Teddy Bears = 40 × 5 = 200
Hence, About 200 teddy bears in the store.
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Find the Laplace Transforms of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex]
Using the definition of the Laplace transform:
[tex]\displaystyle L\left\{\int_0^t \tau \cos(3\tau) \, d\tau\right\} = \int_0^\infty \left(\int_0^t \tau \cos(3\tau) \, d\tau\right) e^{-st} \, dt[/tex]
Reverse the order of integration. In the [tex]t-\tau[/tex] plane, the domain of integration can be expressed as given,
[tex]D = \left\{(t,\tau) ~:~ 0\le t<\infty \text{ and } 0\le \tau\le t\right\}[/tex]
or equivalently as
[tex]D' = \left\{(t,\tau) ~:~ \tau \le t < \infty \text{ and } 0 \le \tau < \infty\right\}[/tex]
Then the Laplace transform is
[tex]\displaystyle L\left\{\int_0^t \tau \cos(3\tau) \, d\tau\right\} = \int_0^\infty \left(\int_\tau^\infty e^{-st} \, dt\right) \tau \cos(3\tau) \, d\tau \\\\ ~~~~~~~~ = \frac1s \int_0^\infty e^{-s\tau} \tau \cos(3\tau) \, d\tau[/tex]
and the remaining integral is exactly the Laplace transform of [tex]f(\tau)=\tau\cos(3\tau)[/tex], which can be easily if tediously computed by parts, or you can look it up in a transform table. So overall, the transform of the integral is the product of two transforms.
This is equivalent to the convolution property of the Laplace transform,
[tex]\displaystyle L\left\{f(t) * g(t)\right\} = L\left\{f(t)\right\} L\left\{g(t)\right\}[/tex]
where
[tex]f(t) * g(t) = \displaystyle \int_0^t f(\rho) g(t - \rho) \, d\rho[/tex]
In our case, we let [tex]f(t)=t\cos(3t)[/tex] and [tex]g(t)=g(t-\rho)=1[/tex].
To find the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex], we can use the properties of the Laplace transform. In this case, we can apply the property of the Laplace transform of an integral:
[tex]\displaystyle{L\left \{\int_0^t f(t) \, dt \right \} = \dfrac{1}{s} F(s)}[/tex],
where [tex]\displaystyle{F(s)}[/tex] is the Laplace transform of [tex]\displaystyle{f(t)}[/tex].
In this case, [tex]\displaystyle{f(t) = t\cos 3t}[/tex]. Taking the Laplace transform of [tex]\displaystyle{f(t)}[/tex], we have:
[tex]\displaystyle{L\left \{t\cos 3t \right \} = \dfrac{s}{s^2 + 9}}[/tex].
Now, applying the property of the Laplace transform of an integral, we can find the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex]:
[tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \} = \dfrac{1}{s} \cdot \dfrac{s}{s^2 + 9} = \dfrac{1}{s^2 + 9} = 1}[/tex].
Therefore, the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex] is 1.
what is
y +2(y-5)=2y+2
Answer:
y = 12Step-by-step explanation:
y +2(y-5)=2y+2
y + 2y - 10 = 2y +2
3y - 10 = 2y +2
3y - 2y = 2 + 10
y = 12
---------------------------------
check
12 + 2 * (12 - 5) = 2 * 12 + 2 (remember PEMDAS)
12 + 24 - 10 = 24 + 2
26 = 26
the answer is good
Use the following function rule to find f(-2).
f(x) = |x-10|
f(-2) =
Jacquelyn earns $60,000 each year at her job. She saves 25% of her income each year. She wants to purchase a house that needs a down-payment of $50,000. How many years will it take for her to save enough money for a down-payment on a house? (Enter your answer below, represented in years. Round any decimals to the nearest tenth.)
Answer: x = 3.3
Step-by-step explanation:
Based on the given conditions, formulate: 60,000 * 25% * x = 50,000
Multiply the monomials: 15000x = 50,000
Divide both sides of the equation by the coefficient of variable: x = 50,000
______
15,000
Cross out the common factor: x 10
3
Round the number: x = 3.3
Answer x = 3.3
a researcher studies a group of 25 preschool children in order to answer questions about the entire population of preschool children. what general categories of statistical techniques will this researcher be using?
The researchers use inferential statistics.
Inferential statistics uses measurement from a sample, comparing groups and making generalizations about the large population. Inferential statistics are based on a test statistic calculated based on a formula. The test statistic along with degrees of freedom to determine the difference between the study population. With inferential statistics, the researcher will draw conclusions from extrapolations.
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the temperature in montreal was -15 degrees . in nyc the temperature was 11 degrees. how many degrees warmer was the temperature in nyc
Answer: 26 degrees
Step-by-step explanation: Count from -15 to 11 or add them up.
The following table summarizes the percent of U.S. who have diabetes and the accuracy of the current medical tests used to detect the disease.
Test positive Test negative Total
Have diabetes
36.1%
1.9%
38%
Do not have diabetes 5.2%
56.8%
62%
What percent of those who do not have diabetes test negative for the disease?
O 10.9%
O 56.8%
091.6%
96.8%
The percentage of Americans who have diabetes and the reliability of the diagnostic. The percentage of those who do not have diabetes test negative is 56.8%.
Give that,
The percentage of Americans who have diabetes and the reliability of the diagnostic procedures now in use are listed in the table below.
There are 3 rows in a tables and 4 column.
1st row,
Diabetes---test positive---test negative---total
2nd row,
Have diabetes---36.1%---1.9%---38%
3rd row,
Do not have diabetes---5.2%---56.8%---62%
We have to find the percentage of those who do not have diabetes test negative for the disease.
See the 3rd row,
In that the percentage of those who do not have diabetes test negative is 56.8%.
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I have to determine the coordinates of the x-intercepts of the parabola. please help I need assistance with this practice problem.
The x-intercept of a graph refers to the points where the graph cuts or intersects the x-axis.
These are the x-values when y is equal to zero.
From the graph provided, the values of x when the graph cuts the x-axis are:
[tex]\begin{gathered} x=-3 \\ and \\ x=-1 \end{gathered}[/tex]Therefore, the coordinates of the x-intercepts are:
[tex](-3,0)\text{ and }(-1,0)[/tex]The answer type is "Two points".
The values in the table represent a function.
f(x)
X
-6
7
4
3
-5
8
3
-5
-2
12
Use the drop-down menus to complete the statements.
The ordered pair given in the first row of the table can
be written using function notation as
f(3) is
f(x) = -5 when xis
1. (-6, 8)
(x coordinate, y coordinate)2. -2
This is the value of f(x) when x=3.3. 4
When x=4, f(x) = -5.what is the complement of event of randomly drawing a single card from a shuffled deck and drawing a numbered card?
The complement of the event is diamond, club or spade.
The complement of an event means " to not choose the mentioned one" .
That is in mathematics we define complement as 1 - E, which is also written as E with a bar, here E represents the event.
In this question we would have to pick a card which is complementary to the heart that is the card needs to be a diamond, spade or a club.
Thus the complement of the event is diamond, club or spade.
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f(x) = 6x³ - 23x² - 6x + 8 if (x-4)
Answer:
(x - 4) (2x - 1)(3x + 2)
Step-by-step explanation:
Dividing:
x - 4)6x^3 - 23x^2 - 6x + 8 (6x^2 + x- 2 <----Quotient
6x^3 -24x^2
x^2 - 6x
x^2 - 4x
-2x + 8
-2x + 8
6x^2 + x - 2
= 6x^2 - 3x + 4x - 2
= 3x(2x - 1) + 2(2x - 1)
= (3x + 2)(2x - 1)
y = x + 2 in standard form
Answer: The answer is x-y = -2
If sides BD and DC have the same length, what is the length of side BC?
The length of side BC, |BC|, is 2 units. The correct option is C. 2 units
Calculating lengthFrom the question, we are to determine the length of side BC
First, we will determine the length of side BD
From Pythagorean theorem, we can write that
|BD|² = |AB|² + |AD|²
From the given information,
|AB| = 1
|AD| = 1
Thus,
|BD|² = 1² + 1²
|BD|² = 1 + 1
|BD|² = 2
|BD| = √2
Also, we can write that
|BC|² = |BD|² + |DC|²
From the given information,
|BD| = |DC|
Thus,
|BC|² = (√2)² + (√2)²
|BC|² = 2 + 2
|BC|² = 4
|BC| = √4
|BC| = 2
Hence, side BC is 2 units
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A recipe requires 2 1/2 of flour. How much flour is needed to triple the recipe?
Answer:
7.5 or 7 1/2
Step-by-step explanation:
A recipe requires 2 1/2 of flour. How much flour is needed to triple the recipe?
3 × 2 1/2 can be written as 3 × 2.5 = 7.5 or 7 1/2
HELP FAST
which is a correct classification of DEF with vertics D(-3,2) E(-2,3) and F(1,0)
The correct classification of DEF is a right-angled scalene triangle.
We are given three vertices D(-3, 2), E(-2, 3), and F(1, 0).The length of the side DE is √[(3-2)² + (-2-(-3))²] = √2.The length of the side EF is √[(0-3)² + (1-(-2))²] = 3√2.The length of the side FD is √[(2-0)² + (-3-1)²] = 2√5.The lengths of all the sides of the triangle are unequal.Thus, DEF is a scalene triangle.Apply the Pythagorean theorem.We notice that :DE² + EF² = FD²(√2)² + (3√2)² = (2√5)²2 + 18 = 2020 = 20Thus, DEF is also a right-angled triangle.Hence, DEF is a right-angled scalene triangle.To learn more about scalene triangle, visit :
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What is the length of the missing side, x?
40 in.
51°
Your answer
74°
35 in.
74°
X
49 in.
55°
Step-by-step explanation:
write the question properly
Four students have rewritten the expression with rational exponent in radical form as shown. Which student is correct?
Sammi VE
Malik √7³
Cassie √x5
Casey √T
The expression with rational exponent in radical form as √x⁵ Cassie's expression is correct.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
We have been given that four students have rewritten the expression with rational exponent in radical form as shown.
As per Sammi's expression: VE
This is an incorrect expression
As per Malik's expression: √7³
This is an incorrect expression
As per Cassie's expression: √x⁵
This is the correct expression
As per Casey's expression: √T
This is an incorrect expression
Thus, the expression with rational exponent in radical form as √x⁵ Cassie's expression is correct.
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describe how to estimate the regression function (equivalently, a,b) by the least-squares principle. notes: you only need to provide a description. this is an example of a nonlinear regression model.
The estimates are used to construct the estimated regression equation:
ŷ = b0 + b1x.
What is the estimation of the regression function?Regression analysis is typically performed for one of two reasons: to estimate the influence of some explanatory variable on the dependent variable or to predict the value of the dependent variable for individuals for whom some information about the explanatory variables is available. Y = mX + b is the equation for simple linear regression, where X is the predictor (independent) variable, m is the estimated slope, and b is the estimated intercept. An estimated regression equation is created using these estimates: ŷ = b0 + b1xA straight line is a good approximation to the relationship between y and x on the graph of the estimated regression equation for simple linear regression.Therefore, the estimates are used to construct the estimated regression equation: ŷ = b0 + b1x.
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Find the domain and range for me please help I need help asp
The domain and the range of the graph are x >= 0 and -∝ < y < ∝, respectivelt
What is the domain of a function?The domain of the function is the set of input values of the graph
What is the range of a function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the domain and the range?The domain
On the graph of the function, we can see that:
The x values start from 0 and it extends indefinitely to the right
This means that the domain is x >= 0
The range
On the graph of the function, we can see that:
The y values extend indefinitely on all sides of the coordinate plane
This means that the range is -∝ < y < ∝
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Nicholas has nickels, dimes and quarters that total $12.30. The number of dimes is 3 more than twice the number of nickels, and the number of quarters is three times the number of nickles. how many coins of each kind does he have?
Using a system of equations, the amounts of each coin that he has is given as follows:
Nickels: 12.Dimes: 27.Quarters: 36.System of equationsThe variables to the system of equations are given as follows:
Variable x: number of nickels.Variable y: number of dimes.Variable z: number of quarters.Nicholas has nickels, dimes and quarters that total $12.30, hence, considering the value of each coin:
0.05x + 0.1y + 0.25z = 12.30.
The number of dimes is 3 more than twice the number of nickels, hence:
y = 2x + 3.
The number of quarters is three times the number of nickles, hence:
z = 3x.
Then we can solve for x as follows:
0.05x + 0.1y + 0.25z = 12.30.
0.05x + 0.1(2x + 3) + 0.25(3x) = 12.30.
x = 12. (nickels)
Then the other amounts are as follows:
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16) Indicate whether or not 343 belongs to. each set of numbers.
rational. yes or no
irrational. yes or no
integer. yes or no
whole. yes or no
natural. yes or no
The sets that number 343 belongs to are:
Rational number: YesIrrational number: NoIntegers: YesWhole numbers: YesNatural numbers: YesWhat are rational numbers?Any number that can be expressed as a fraction and where the denominator (the bottom number) and the numerator (the top number) are both integers is considered a rational number. In other words, p/q, where p and q are both integers and q 0, can be used to represent a rational number. If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Among the rational number, examples are 1/3, 2/4, 1/5, 9/3, and so forth.So, 343 is:
Rational number (written in fractions): YesIrrational number (cannot be written in fractions): NoIntegers (Non-fraction, positive, negative, or zero): YesWhole numbers (Positive, negative, and zero): YesNatural numbers (0, 1, 2, 3, 4, 5.....): YesTherefore, the sets that number 343 belongs to are:
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Please help me please
To prove ∠1 = ∠3.
What are parallel lines?Parallel lines are a grouping of two or more lines that all lie in the same plane but never cross. Both of them have the same slope and are equally spaced apart.
Numerous pairs of angles are created whenever any two parallel lines are intersected by a third line known as a transversal. The other angles are supplementary while some are congruent (equal). The parallel lines L1 and L2, which are divided by a transversal, can be seen in the following figure.
Given : [tex]l||k , m||n[/tex]
∠1= ∠2 {alternate interior angles}
∠2=∠3 {corresponding angles are equal because k is parallel to l }
Thus from the above two equations :
∠1 = ∠3
Hence, proved .
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Write an equation of the line passing through point P (0,1) that is parallel to the line y=-2x+3
The equation of the line passing through point P (0,1) = y=2x-1
What is Equation of line ?
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.
Rise over run = (y+1)/(x-0)
=(y+1)/x =-2
slope is (y+1)/(x-0) =(y+1)/x
=-2;
-2x=y+1, or
y+2x =-1, or
y=-2x-1
in the form of the slope intercept
The parallel line with the value of y=-2x+3 has been moved down by 4 units. The point at which this line crossed the y-axis was y=3. Now, with a 4 downshift, it crosses the y-axis at y=1.
Plugging the location (0,1) into the new equation:
y=2x-1 yields
1 = 2(0)-1
to validate the math.
Hence, the Equation of line passing through point P(0,1) is y=2x-1
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A motor boat whose speed is 18 km/h in still water. It takes 1 hour more to go
24 km upstream than to return downstream to the same spot. Find the speed of the boat?
The speed of the stream is 6 [tex]km/h[/tex]
Let the speed of the stream be x km/h.
Therefore, the speed of the boat upstream = (18 – x) km/h, and the speed of the boat
downstream = (18 + x) km/h.
The time is taken to go upstream = distance/speed
[tex]24/(18-x)[/tex] hours.
Similarly, the time is taken to go downstream =
[tex]24/(18+x)[/tex] hours.
According to the question,
[tex]24/(18-x) - 24/(18+x) = 1[/tex]
[tex]x^{2} +48x-324=0[/tex]
Using the quadratic formula, we get
[tex]x=\frac{-48+\sqrt{48^{2}+1296 } }{2}[/tex]
x = 6 or -54
Since x is the speed of the stream, it cannot be negative. So, we ignore the root x = – 54.
Hence the speed of the stream is 6 km/h.
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double the difference of w and u, then multiply the result by v
Translating the given words into algebraic expression it becomes 2v(w-u) .
In the question ,
the word phrase is given as" double the difference of w and u, and then multiply the result by v "
for translating into algebraic expression , we proceed step by step
step 1 : difference of w and u
we get , (w - u)
step 2 : double the difference of w and u ,
we get , 2(w-u)
step 3 : then multiply the result by v ,
we get , 2(w-u)*v
= 2v(w-u)
Therefore , translating the given words into algebraic expression , the expression is 2v(w-u) .
The given question is incomplete , the complete question is
Translate the following word phrase into an algebraic expression , "double the difference of w and u, then multiply the result by v "
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Which of the following equations represents the parabola with vertex at (3, 2) and directrix y = 4?
a (x − 3)2 = −8(y − 2)
b (x + 3)2 = 8(y + 2)
c (y − 2)2 = −4(x − 3)
d (y + 2)2 = 4(x + 3)
The equation of parabola is (x − 3)² = −8(y − 2).
What is parabola?A parabola is a U-shaped curve that is drawn for a quadratic function, f(x) = ax²+ bx + c. The graph of the parabola is downward (or opens down), when the value of a is less than 0, a < 0. The graph of parabola is upward (or opens up) when the value of a is more than 0, a > 0.
Given:
Vertex = (3, 2)
Directrix, y =4
line of symmetry is the Y value in the vertex = 2
directrix, y= 2 - p
p = -2
and, a= 1/4p = -1/8
and, focus = (3, (2-2)) = (2, 0)
Now, equation of parabola
y= -1/8 (x- 3)² + 2
-8y = (x- 3)² + 2
(x − 3)² = −8(y − 2)
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Please help…..will give brainliest
Answer:
p= -8
Step-by-step explanation:
[tex]10p + 5 = \frac{18p - 6}{2} \\ multiply \: ech \: sde \: by \: 2 \\ 20p + 10 = 18p - 6 \\ 20p - 18p = - 6 - 10 \\ 2p = - 16 \\ p = - 8[/tex]
A problem states: "There are 9 more children than parents in a room. There are 25 people in the room in all. How many children are there in the room?"
What are the unknowns in this problem?
Responses
the total number of people in the room
the total number of people in the room
the total number of parents in the room
the total number of parents in the room
the total number of children in the room
the total number of children in the room
the total number of children and the total number of parents in the room
By solving a system of equations, we can see that there are 17 children and 8 parents in the room.
How to get the total number of children in the room?Let's define the variables:
x = number of children.
y = number of parents.
We know that there are 9 more children than parents, then:
x = y + 9
And there is a total of 25 people, so:
x + y = 25
So we have a system of equations:
x = y + 9
x + y = 25
Replacing the first equation into the second one, we get:
(y +9) + y = 25
2y + 9 = 25
2y = 25 - 9 = 16
y = 16/2 = 8
then the value of x is:
x = y + 9 = 8 + 9 = 17
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-f(4) =
If g(x) = 2, x =
A mathematical connection known as a function is one in which the values of one or more independent variables determine the values of a single dependent variable. Function implies that the independent variable affects the dependent variable (s).
Explain the functions and variables in mathematics? A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.We have seen that functions can be stored in variables, and we shall investigate this further later. In JavaScript, a value called an object is a container for additional data like integers, characters, functions, and other objects.We can avoid repeatedly writing the same logic or code in a program by using functions. C functions can be called from anywhere in a program and at any number of times. When a large C program is broken up into several functions, we can simply track it.
The answer is -11
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You have been assigned to work with a partner on a word processing assignment over the weekend. You both have Microsoft Online
access. When you are finished with your section, your partner will also need add in their portion of the project. What is the most efficient
way to send the document?
Use the Share command.
Print it out.
Export to PowerPoint.
Save it as an ODT file.