Sara is competing in a 200 m race. She runs at a constant speed of 4.6 m/s for the first 50 m, then 4.2 m/s for 10 seconds. The remainder of the race takes her 23 seconds to complete. What is Sara's average speed for the entire race to 1 dp?

Answer:

Let x be the number of guppies Percious can purchase.

We know that the total cost of the goldfish, starfish and guppies is less than or equal to $80.

We can use this information to write an inequality:

32 + 12 + 6x <= 80

This inequality represents the total cost of the goldfish, starfish, and guppies.

By solving this inequality we can find the number of guppies Percious can purchase.

To solve this inequality, we can first simplify it by combining like terms:

44 + 6x <= 80

Then we can subtract 44 from both sides:

6x <= 36

And finally, we divide both sides by 6:

x <= 6

So, Percious can purchase a maximum of 6 guppies if she wants to spend all of her money.

x is less than or equal to 6.

Step-by-step explanation:

Let x be the number of guppies Percious can purchase.

We know that the total cost of the goldfish, starfish and guppies is less than or equal to $80.

We can use this information to write an inequality:

32 + 12 + 6x <= 80

This inequality represents the total cost of the goldfish, starfish, and guppies.

By solving this inequality we can find the number of guppies Percious can purchase.

To solve this inequality, we can first simplify it by combining like terms:

44 + 6x <= 80

Then we can subtract 44 from both sides:

6x <= 36

And finally, we divide both sides by 6:

x <= 6

So, Percious can purchase a maximum of 6 guppies if she wants to spend all of her money.

x is less than or equal to 6.

Answer:

The graph that shows the translation f(x) = f(x) + 1 is the graph that is shifted upward by one unit on the y-axis. All the points on the graph have been moved upward by one unit, but the shape of the graph remains the same as the parent function.

The dotted line graph that shows the translation f(x) = f(x) + 1 is the one where the graph is shifted upward by one unit on the y-axis.

The angles which measure 20 degrees are∠1 ,∠5 ,∠7 ,∠9 ,∠11 ,∠14 ,∠16. The solution has been obtained using the properties of parallel lines.

Parallel lines are any two or more lines that lie in the same plane, are equally spaced apart, and never cross one another.

We are given t || x and k || w and m∠3 = 20°

Using the properties of parallel lines, we get -

∠3 = ∠1            (As these are vertically opposite angles)

∠3 = ∠5           (As these are alternate interior angles)                

∠3 = ∠7             (As these are corresponding angles )

Now,

∠4 = 180 - ∠3                     (As they form a linear pair)

∠10 = 180 - ∠9                    (As they form a linear pair)

Also,

∠10 = ∠4                            (Parallelogram's opposite angles are same)

So,

180 - ∠9 = 180 - ∠3

∠3 = ∠9                                                       .... [ii]

∠9 = ∠11               (As these are vertically opposite angles)

∠3 = ∠11               ( from [ii] )                                           .... [iii]

∠11 = ∠14               (As these are alternate interior angles)

∠3 = ∠14               ( from [iii] )                                               .... [iv]

∠14 = ∠16               (As these are vertically opposite angles)

∠3 = ∠16               ( from [iv] )    

Hence, the angles which measure 20 degrees are

∠1 ,∠5 ,∠7 ,∠9 ,∠11 ,∠14 ,∠16.

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Answer:

4+3=7

-2+3=7

Step-by-step explanation:

Answer:

The third option.

Step-by-step explanation:

Lets write the length as L and the width as W.

Given, L = W - 4

or L - W = - 4

Perimeter of a rectangle = 2( L + W)

44 = 2 (L + W)

L + W = 22

L - W = -4

2L = 18 (adding the two equations)

L = 9

W = 13

So, the answer is the third option.

Cheers

Answer: 464

Step-by-step explanation: 232+232 = 464

Answer:

464 is answer very easy.........

The simplified value of the equation is w = -1.

To simplify means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.

Given equation w/4 + 11/12 = 1/2 - w/6

the equation is written as,

w/4 + w/6 = 1/2 - 11/12

solving by LCM

(3w + 2w)/12 = (6 - 11)/12

5w = -5

w = -5/5

w = -1

Therefore the value of w is -1.

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There are 36 fluid ounces in 4.5 cups

Keisha reads a label on a measuring cup

The reading shows that 16 fluid ounces is the same as two cups

Therefore the number of fluid ounces in 4.5 cups can be calculated as follows

16/2

= 8

8 × 4.5

= 36

Hence there are 36 fluid ounces in 4.5 cups

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A circle with a radius of three and a center at (-1, 4) is a conic section with the parametric equations X=3cos(t)-1 and Y=3sin(t)+4.

The circle, the ellipse, the parabola, and the hyperbola are examples of conic sections.

Using a third variable (t or ), parametric equations are utilized to express the x and y variables in terms of a less complex way.

The parametric equation for a circle is given by: x=r cos(t) +h, y=r sin(t) +k, where r is the radius of the circle and (h, k) is the center of the circle. The equation for a circle is (x- h)2+(y- k)2 = r2.

A circle with a radius of three and a center at (-1, 4) is a conic section with the parametric equations X=3cos(t)-1 and Y=3sin(t)+4.

The circle's equation is (x + 1)2 + (y - 4)2 = 32.

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Answer:

Step-by-step explanation:

The terminal point of the vector a=⟨4,3⟩ based at P=(5,2) is the point (9,5). This can be calculated by adding the components of the vector to the corresponding components of the base point:

Terminal point = (x,y) = (Px + ax, Py + ay)

      = (5 + 4, 2 + 3)

      = (9,5)

Answer:

Step-by-step explanation:
✔️For determining terminal point of vector a=(4,3)  whose base is at the point P=(5,2).

✔️ Add to point P and that

✔️Point that the vector is pointing at to find the terminal point....

➖So we can say That

✔️Since the tail of the vector a=(4,1) a=(4,1) is a point P(2,3) then the tip of the vector, the terminal point woll be :-

(5,2)+(4,3)=(9,6)

your welcome !

Using multiplication operation, the TRUE statement about the number of kilograms of dog food in the bag is A. There are approximately 55 kilograms of dog food in the bag, because 1/2.2 = 55/25.

The number of kilograms of dog food in the bag is determined using the multiplication operation.

The multiplication operation is one of the basic mathematical operations, including addition, subtraction, and division.

The multiplication operation involves multiplying the multiplicand by the multiplier to get a result called the product after the equal sign.

The pounds of dog food in a bag = 25 pounds

Approximately 2.2 kilograms = 1 pound

The number of kilograms = 25 x 2.2

= 55 pounds

Thus, Option A is correct since 1/2.2 equals 55/25, based on the multiplication operation.

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Solution for the given System of linear equation is:

Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods to solving systems of equations: graphing, substitution, elimination and matrices.

Given,  the system of linear equations on the left with its solution type on the right

For  Y=2x-1 and Y=2x+1

Adding both equation,  we will get y = 4x

Thus, these equations have infinite number of solution

For 2x - y = 7 and 3x + y = 3

Adding these equations

5x = 10

x= 2

Substitute the value in equation 1

y = -3

Thus, solution is (2, - 3)

therefore, the Solution for the given System of linear equation is:

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Complete question:

The diameter of the wheel of the truck is 3.33 feet.

A straight line that runs through the sideways of a body or figure, particularly a circle or sphere, is called as a diameter of a circle or sphere.

The distance around the wheel of a truck is 10.45 feet.

Let the diameter of the wheel = d feet.

Circumference of the wheel

= Distance around the wheel,

πd = 10.45 feet.

d = (10.45/π) feet.

Here, we take the π = 3.14.

So,

d = 3.326

d = 3.33

Therefore, the diameter is 3.33 feet.

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Answer:

t = I/(Pr)

Step-by-step explanation:

We divide P*r on both sides to isolate t and we get t=I/(P*r)

After transformation, the point (-1,2) in the image would be (-1,-2)

Each transformation applied to the prior image is combined into a composition of transformations. The result of a translation is identical to a composition of reflections across parallel lines (twice the distance between the parallel lines). The composite transformation is carried out by multiplying the matrix in order from the right to the left side if it is represented as a column. The output from the preceding matrix is multiplied by the new matrix that will follow.

First, we must mirror the point (-1, 2) around the line y=-x.

(X, Y) is the rule (-y,-x)

you obtain (-1,2)—>(-2,1) (-2,1)

At this point, you must rotate (-2,1) by 90 degrees.

(X, Y) is the rule ( -y,x)

so (-2,1)—> (-1,-2) (-1,-2)

After transformation, the point (-1,2) in the image would be (-1,-2)

The complete question is,

What is the image point of (-1,2) after the transformation R 90° ry=-x

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Answer: We can write an inequality to show how many more inches Bobby needs to grow to reach his desired height by using the following information:

Bobby hopes that he will someday be more than 72 inches tall.

He is currently 59 inches tall.

We can use the inequality x + 59 > 72, where x is the number of inches Bobby needs to grow to reach his desired height.

This inequality represents the total height (x + 59) being greater than the desired height (72).

To solve this inequality, we can subtract 59 from both sides:

x > 72 - 59

x > 13

So, Bobby needs to grow 13 inches or more to reach his desired height.

Step-by-step explanation:

The rectangular bin has a depth of 20 feet.

A cuboid is a three-dimensional shape with rectangles on all sides. A cuboid has six faces, eight vertices, and twelve edges. All of the angles formed at a cuboid's vertices are right angles. The opposing edges are perpendicular to each other.

For the given situation,

A rectangular bin is in the shape of a cuboid.

Volume of the rectangular bin, V = 1200 cubic feet

Length of the rectangular bin ,l = 10 feet

Width of the rectangular bin,w = 6 feet

Let the height of the rectangular bin be h.

The formula of volume of cuboid is

[tex]v=lwh[/tex]

Now substitute the above values,

⇒ 1200= (10)(6)h

⇒ [tex]h=\frac{1200}{60}[/tex]

⇒ h= 20

Hence we can conclude that the rectangular bin is 20 feet deep.

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The depth of the box is found through the volume formula for a rectangular prism, which involves multiplying the length, width and depth. Knowing the volume when half-filled, and the length and width, we can calculate the box is 10 feet deep.

This problem deals with the concept of volume in mathematics. First, the formula for the volume of a rectangular prism (or a box) is length multiplied by width multiplied by height. In this case, we know that the box is half filled with grain and that the total volume of that grain is 200 cubic feet. So, if the box was filled completely, it would have a volume of twice that, or 400 cubic feet.

Now we know that the box's volume is 400 cubic feet and its length is 8 feet and width is 5 feet. So to find the height (which is what we're calling 'depth' in this case), we can use our volume formula. We divide the total volume by the product of the length and width (400/40) to find the height or depth, resulting in a depth of 10 feet.

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Answer:

To verify that [n+3]! / n! = (n+1), we can use the definition of factorial:

[n+3]! = (n+3) * (n+2) * (n+1) * n!

And we can cancel out n! from both sides of the equation:

(n+3) * (n+2) * (n+1) = n+1

Which is true, and thus [n+3]! / n! = (n+1) holds true.

Another way to verify this is by simplifying the RHS and LHS

(n+1) = (n+1)

And the LHS,

(n+3)! = (n+3)(n+2)(n+1)n! = (n+1)(n+2)(n+3)n! = (n+1)(n+2)(n+3)!/n!

which is also equal to (n+1)

So, [n+3]! / n! = (n+1) is true.

Answer: 27,800.0 cm[tex]^{3}[/tex] / 1,696.5 cu in.

Step-by-step explanation:

So Basically, If the Diameter is 12 and the height is 15 inches, the radius will be 6 inches making the Volume of the cylinder 1696.46 cu in.

Now if we were to round that to the nearest place it'd be 1,696.5 cu in.

However, If you want the answer in cm[tex]^{3}[/tex] it would be 27,800 cm making the rounded value 27,800.0 cm[tex]^{3}[/tex].

Hope that helped!

Answer: D) 7 3/4

Step-by-step explanation:

With averages, we add all the values and divide by the number of values. Here, we know three out of the four days, let's label the day we don't know x. There are four days, so we can divide by four. 7 1/4 is the average, so we can set the equation equal to 7 1/4.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x) / 4

Let's multiply both sides by 4 to get rid of the fraction. Let's also add what is in the parentheses

29 = 21 1/4 + x

Now we can isolate x by subtracting 29-21 1/4

so

x = 7 3/4 thus the answer is D

Answer:

D) 7 3/4

Step-by-step explanation:

Let x = amount of last feeding.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x)/4

4 × 7 1/4 = 7 1/2 + 7 3/8 + 6 3/8 + x

28 + 1 = 7 4/8 + 7 3/8 + 6 3/8 + x

29 = 20 10/8 + x

(20 10/8 is the same as 20 + 10/8 = 20 + 8/8 + 2/8 = 20 + 1 + 1/4 = 21 + 1/4 = 21 1/4)

29 = 21 2/8 + x

29 = 21 1/4 + x

x = 29 - 21 1/4

x = 28 4/4 - 21 1/4

x = 7 3/4

Answer: 7 3/4

There are 45 pounds are needed for 6045 square​ feet.

What is pounds?

The United Kingdom and nine of its associated territories use the sterling as their currency. The pound is the primary unit of sterling, and the term "pound" is also frequently used to refer to the British pound or the pound sterling in international contexts.

Given:

3 pounds of grass seed cover 403 square​ feet.

We have to find the how many pounds are needed for 6045 square​ feet.

As 3 pounds of grass seed cover 403 square​ feet.

⇒ 403/3 = 134.33

⇒  1 pound of grass seed cover 134.33 square feet.

Let x pounds needed for 6045 square feet.

⇒ x = 6045 / 134.33 = 45

Hence, there are 45 pounds are needed for 6045 square​ feet.

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Considering the figure the value of angle b is

According to the vertical angle theorem, the opposing angles of two crossing lines must have the same value, or be congruent.

hence angle a = angle y

Then from exterior angle of a triangle theorem: If a triangle's side is created, the outside angle that results is equal to the sum of the two opposite internal angles.

angle b = angle a + 90

= 34 + 90

= 124 degrees

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Answer:

1) Quadrilateral ABCD is translated 5 units and 4 units down, then reflected in the y-axis. This will result in congruent figures. Translation only moves the figure without changing the size or shape, and reflection in the y-axis will mirror the figure across the y-axis without altering its size or shape. Since both operations preserve the size and shape of the figure, the resulting figure will be congruent to the original.

2) ΔJKL is dilated by a scale factor of 2 and then rotated 180° about the origin. This will result in congruent figures. Dilation by a scale factor of 2 will double the size of the triangle while maintaining its shape, and rotation by 180° about the origin will flip the triangle over the origin while maintaining its shape. Since both operations preserve the size and shape of the figure, the resulting figure will be congruent to the original.

3) Line segment XY is rotated 90° about the origin, dilated by a scale factor of -1/2, and then reflected in the line x = 5. This will result in similar figures. Rotation by 90° about the origin will rotate the line segment by 90 degrees, dilated by a scale factor of -1/2 will shrink the size by half but with a change in direction and reflection in the line x = 5 will mirror the figure across the x=5 line without altering its size or shape. Since all the operations maintain the shape of the figure but the size changes, the resulting figure will be similar to the original one.

Translation and reflection doesn't change the shape or size of the figure, therefore the resulting figure is congruent to the initial one.

Rotation doesn't change the shape of the figure, but dilation changes the size, therefore the resulting figure is similar to the initial one.

Rotation and reflection don't change, but dilation changes the size, therefore the resulting segment is similar to the initial one.

Answer:

15p + 10

Step-by-step explanation:

5 (3p+2)

15p + 10

Answer:

f(-4) = -36

Step-by-step explanation:

Step-by-step explanation:

A function assigns the value of each element of one set to the other specific element of another set. The value of the function when the value of x is -4 is 92.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

Given that F(x)=3x²-10x+4, therefore, the value of the function can be calculated by substituting the value of x as -4.

Therefore, the value of the function when the value of x is -4  can be calculated as shown below,

F(x) = 3x² - 10x + 4

F(-4) = 3(-4)² - 10(-4) + 4

= 3(16)  + 40 + 4

= 48 + 40 + 4

= 92

Hence, the value of the function when the value of x is -4 is 92.

The angles in the parallelogram are as calculated below

A parallelogram is a quadrilateral with opposite sides parallel. This means that both pairs of opposite sides are parallel and of equal length. The opposite angles of a parallelogram are also equal in measure.

m ∠BEA = 60° (alternate angles)

m ∠BAE = 42° (alternate angles)

m ∠DAE = 40° (alternate angles)

m ∠ABE = 180 - m ∠BEA - m ∠BAE = 78° (angle in a triangle)

m ∠CBE = 78° (vertically opposite angles)

m ∠ABD = 180 - m ∠ABE = 102° (angle on a straight line)

m ∠CBE = 102° (vertically opposite angles)

m ∠BEC = 180 - m ∠CBE - m ∠BEC = 38° (angle in a triangle)

m ∠ADB = 38°  (alternate angles)

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Answer:

1.806 (to the nearest thousandth)

Step-by-step explanation:

1.806 (to the nearest thousandth)

The number 1.80642 would round down to 1.806

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

We need to round  1.80642 to the nearest hundredth,

We can see that the 1.80642 is below 2 so it goes down, and it rounds down to 1.80642 instead of, 14.62 then that would round up to the decimal is higher than 1.

1.80642 rounded to the nearest thousandth is 1.806.

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So on solving provided question we can say that the probability 20% of these coins are pre-1910, 15% are between 1910 and 1950, and the remaining 75% are post-1950.

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

Emma has a collation of 240 coins.

Of these coins, 20% are dated before 1910,  15% are dated between 1910 and 1950 and  the remainder are dated after 1950.

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Answer:

top right graph

Step-by-step explanation:

5y=-10x+20

y=-2x+4