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The lower bound is 147.5 and the upper bound is 152.5.

Given the weight of an apple 150 g rounded to the nearest 5g.

We have to find lower bound and upper bound.

Lower bound is an element less than or equal to all the elements in a given set.

Upper bound is an element greater than all the elements in a given set.

Lower bound= Number 1- (Number nearest to  which number 1 is rounded)/2

Upper bound=Number 1+(number nearest to which number 1 is rounded)/2

Weight of an apple =150 g

Lower bound=150-5/2

=150-2.5

=147.5

Upper bound=150+5/2

=150+2.5

=152.5

Hence the lower bound is 147.5 and upper bound is 152.5.

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[tex]x {}^{2} - 8x - 9 = 0 \\ x + y = 8 \\ xy = - 9[/tex]

[tex]g(x) = x {}^{2} - 7x + 12 \\ g(6) = 36 - 42 + 12 = 6 \\ g( - 7) = 49 + 49 + 12 = 110 \\ g( - 3) = 9 + 21 + 12 = 42 \\ g(4) = 16 - 28 + 12 = 0[/tex]

b

Answer:

Question 1:The correct answer is C. -1 and 9

Question 2: The correct answer is D.4

Question 3: The correct answer is C. The x-intercept of (5,0) and y-intercept of (0,10)

Question 4: The correct answer is B. True

Question 5: The correct answer is b.

Answer:

Domain: All Real Numbers Range: All Real Numbers

Step-by-step explanation:

The domain and range is going to be infinite. The linear function will be using the x and y- axis in order to continue being a function. The y-intercept will be -2 on the y-axis. I recommend using the rise-over-run method for your slope value. from the point (0, -2) on the y-axis. Go up two on the y-axis, and right 7 on the x-axis.

Sorry, it may be difficult to explain through words.

Answer: [tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}[/tex]

Step-by-step explanation:

We can rewrite the left hand side as a perfect square, more specifically

[tex]\left(x+\frac{b}{2a} \right)^2[/tex]

So, taking the square root of both sides,

[tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}[/tex]

Answer:

Therefore , 25 ans.

The length of the hypotenuse of right triangle ΔDEF is 50.44 units

The hypotenuse side can be found using Pythagoras theorem,

Therefore,

c² = a² + b²

where

Therefore,

x² = 39² + 32²

x² = 1521 + 1024

x = √2545

x = 50.4479930225

x = 50.44

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The company's profit in fifth month will be $506.25

Profit : The gain in an expenditure, that is when the return is higher than the original amount, then the gained extra amount is called profit.

Example : If someone sell a toy of $10 in $15, then he gained profit & his profit is $(15-10) = $5.

A company earns a profit of $100 the first month it is in business.

Every month after that, the company earns a profit that is 1.5 times the previous month's profit.

In 1st Month,

Profit = $100

In 2nd Month,

Profit = 1.5 times of profit of 1st month

         = 1.5 × $100

         = $150

In 3rd Month,

Profit = 1.5 times of the profit of 2nd month

         = 1.5 × $150

         = $225

In 4th Month,

Profit = 1.5 times of the profit of 3rd month

         = 1.5 × $225

         = $337.5

In 5th Month,

Profit = 1.5 times of the profit of 4th month

         = 1.5 × $337.5

         = $506.25

So, the profit of 5th month = $506.25

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Number of males in the meet were 8.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

Let the number of males be x.

∴ Number of females = x + 7

Total number of people attending meet = Number of male +

                                                                    Number of  females

23 = x + x + 7

23 = 2x + 7

16 = 2x

x = 8.

Thus number of males in the meet were 8.

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Using it's concept, it is found that the approximate perimeter of the front of the garage is:

A. about 36 ft.

The perimeter of a figure is given by the total length of it's boundary.

In this problem, we have that:

[tex]t = \sqrt{3^2 + 5^2} = 5.83[/tex]

Hence the perimeter of the figure is:

P = 10 + 2 x 7 + 2 x 5.83 = 35.66.

Rounding, it is of about 36 ft, hence option A is correct.

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Step-by-step explanation:

The polynomial highest degree is 2 so the degree is 2.

The binomial have three terms so it is a trinomial.

⊱________________________________________________________⊰

Answer:

Step-by-step explanation:

[tex]\large\begin{gathered} \sf{36=19+17. 19 \ and \ 17 \ are}\\ \sf{\ both \ primes, \ because \ they're \ only \ divisible \ by \ 1 \ and \ themselves} \\ \sf{ 80=73+7. \ Again, \ 73 \ and \ 7 \ \underline{ARE} \ prime. \end{gathered}}[/tex].

Done!!

⊰________________________________________________________⊱

Answer: 3491.91 radians

Step-by-step explanation:

The total distance in inches traveled by car = 63,360 inches (1 mile)

Total Revolution made by tire through traveling =

[tex]=\frac{63360}{\pi *36.30}[/tex]

We know 1 revolution angle made by tire = 2π radian (360 degrees/1 revolution of unit circle)

In   [tex]\frac{63360}{\pi *36.30}[/tex] ,

the revolution angle made by the tire =

[tex]=2\pi * \frac{63360}{\pi 36.60}[/tex]

[tex]=2 * \frac{63360}{ 36.60}[/tex]

[tex]= 3491.91[/tex] radian

The missing dimension is x + 4

The given parameters are:

Area = 4x^2 + 13x - 12

Length = 4x - 3

The width is calculated using:

Width = Area/Length

This gives

Width = (4x^2 + 13x - 12)/(4x - 3)

Expand

Width = (4x^2 + 16x - 3x - 12)/(4x - 3)

Factorize

Width = (4x(x + 4) - 3(x + 4)/(4x - 3)

Factor out x + 4

Width = (4x - 3)(x + 4)/(4x - 3)

Cancel out the common factor

Width = x + 4

Hence, the missing dimension is x + 4

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Answer:

The volume of the prism increased by a factor of 64.

Step-by-step explanation:

Given that the original prism and the increased prism are similar, we have that the scale factor is:

Area ∝  (length of side) x (length of side)

If the area increases by a factor of 16, each side increases by a scale factor of √16 = 4. Regarding the volume:

Volume ∝ (length of side) x (length of side) x (length of side)

Thus the increase factor for the volume, in this case, is 4 x 4 x 4 = 64.

Answer:

(8,-3)

Step-by-step explanation:

Midpoint Formula: [tex](\frac{x^{1}+x^{2} }{2}, \frac{y^{1} +y^{2} }{{2} } )[/tex]

Plug in your numbers from the coordinates:

(10+6/2, -7+1/2)

(16/2, -6/2)

(8,-3)

In order to move a the constant terms to the right hand side, we need to subtract 0.4 from both sides of the equation.

In an equation, the constant terms are those terms that do not have any alphabet attached to them. In this case, 4 and 0.4 are constant terms.

In order to move a the constant terms to the right hand side, we need to subtract 0.4 from both sides of the equation thus;

-9x + 0.4 - 0.4 = 4 - 0.4

-9x = 3.6

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The set of all input values of a function is the domain of the function

A function relates an input to an output.

A function defines a relationship between one variable (the independent variable) and another variable.

The set of all input values of a function is the domain of the function.

The domain of a function are also called independent variables.

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Answer:

B = (-1, 0)

C = (1, 0)

Step-by-step explanation:

Properties of an Equilateral Triangle

Given:

Drawing an altitude from vertex A divides the triangle into two 30-60-90 triangles.

A 30-60-90 triangle is special right-angled triangle where:

Therefore, the formula for the sides is: b : b√3 : 2b, where:

As Vertex A has the co-ordinates (0, √3), the side opposite the 60° angle is √3 units.

Using the ratios to find b (shortest side length):

b√3 = √3  ⇒  b = 1

As the altitude divides BC into two equal line segments, and the length of the shortest side of the right triangles is 1 unit, the coordinates of B are C are:

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The Simplified algebraic expression for the statement "n divided by 2 plus five minus n" is given by 5-(n/2).

Algebraic Expression is a mathematical expression involving variables, Numbers, other mathematical quantities, and mathematical operations and combinations of them.

Here given statement is "n divided by 2 plus five minus n"

Now we have to write the above given statement as simplified algebraic expression.

"n divided by 2" is given by = n/2

then "n divided by 2 plus five" is given by = (n/2)+5

there after "n divided by 2 plus five minus n" is given by = (n/2)+5-n

Simplifying the total algebraic expression we get,

(n/2)+5-n = 5-{n-(n/2)} = 5-((2n-n)/2) = 5-(n/2)

Hence the suitable Simplified algebraic expression for the given statement is given by = 5-(n/2)

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Answer:

706.858347

Step-by-step explanation:

Answer:

1080.

Step-by-step explanation:

0.00025 tonnes = 0.00025 * 1000 = 0.25 kg.

Total number of packets

(3 *90) / 0.25

= 12*90

= 1080.

Both the given statements are true. The figure is given below.

We need to determine whether the stated conclusion is valid based on the given information.

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

Given: If a point is the midpoint of a segment, then it divides the segment into two congruent segments. R is the midpoint of QS.

Conclusion: QR=RS.

Given: If a point is the midpoint of a segment, then it divides the segment into two congruent segments. AB=BC

Conclusion: B divides AC into two congruent segments

Both the given statements are true. The figure is given below.

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Answer:

D = 12

Step-by-step explanation:

Side ST is corresponding to side QT. 9" / 3" = 3

3 is the proportion between the two triangles.

Side PT is the corresponding side to side RT.

PT = 4" x 3 = 12"

Answer: 1.095

Step-by-step explanation:

The function is increasing, so the rate of change must be greater than 1.

Answer:

They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH.

Step-by-step explanation:

Using the p-value method, the decision rule is:

Depends on if the p-value is less or more than the significance level:

In this problem, we have a two-tailed test, as we are testing if the mean is different of a value. For a significance level of 0.1, the critical value of z(when a p-value of 0.1 is obtained) is of |z| = 1.645, hence the decision rule is:

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[tex]take \: some \: values \\ h(1) = 5.5 \times |1| = 5.5 \times 1 = 5.5 \\h(2) = 5.5 \times |2| = 5.5 \times 2 = 11 \\ h(4) = 5.5 \times |4| = 5.5 \times 4= 22[/tex]

Answer:

43

Step-by-step explanation:

52-9=43