A square gate has a brace 3.5 feet long.
Approximately how wide is the gate?
F. 2.0 feet
3.5 ft
G. 2.5 feet
H. 4.9 feet
J. 6.1 feet
Answer

Answer:

the dimensions of the poster with the smallest area is 36cm by 54cm

Step-by-step explanation:

✓Let us represent the WIDTH of the printed material on the poster as "x"

✓Let us represent the HEIGHT of the printed material on the poster as "y"

✓ The given AREA is given as 864 cm2

Then we have

864 cm2= xy ...................eqn(1)

We can make "y" subject of the formula.

y= 864/x .......................eqn(2)

✓The total height the big poster which includes the 9cm margin that is at the bottom as well as the top is

(y+18)

✓The total width of the poster which includes the 6cm margin that is at the bottom as well as the top is

(x+12)

✓Then AREA OF THE TOTAL poster

A= (y+18)(x+12) ...................eqn(3)

Substitute eqn (2) into eqn(3)

A= ( 18+ 864/x)(x+12)

We can now simplify by opening the bracket, as

A=18x +1080 +10368/x

A= 18x +10368/x +1080

Let us find the first derivative of A which is A'

A'= 18-(10368/x²)

If we set A' =0

Then

0= 18- (10368/x²)

18= (10368/x²)

x²= 10368/18

x²= 576

x=√576

x=24

The second derivatives will be A"= 2(10368)/x³ and this will be positive for x> 0, and here A is concave up and x=24 is can be regarded as a minimum

The value of "y" when x=24 can now be be calculated using eqn(2)

y= 864/x

y= 864/24

y=36cm

✓The total width of the poster= (x+12)

= 24+12=36cm

✓The total height big the poster= (y+18)=36+18=54cm

the dimensions of the poster with the smallest area is 36cm by 54cm

Answer:

The total width of the paper \(=36 cm.\)

The total height of the paper \(=54cm\)

Step-by-step explanation:

Given information:

Top margin of the paper = 9 \(cm\\\)

Bottom margin of the paper = 6 \(cm\\\)

Area of the printed material = \(864\) \(cm^2\)

Let, the width of the printed material = \(x\)

And the height of the printed material = \(y\)

So, Area \(x \times y=864\) \(cm^2\)

After including margins;

Width of the paper \(= (x+12)\)

Height of the paper \(= (y+18)\)

Area \((A) = (y+18) (x+12)\)

\(A=18x+(10368/x)+1080\\\)

Take first derivative:

\(A'= 18- (10368/x^2)\)

When \(A'=0\)

Then,

\(18-(10368/x^2)=0\\x^2=576\\x=24\)

Now ,when we take second derivative and check if it is positive or not ,

We find that it is grater than zero so the obtained value can be consider as minimum and can be proceed for further solution.

Hence ,

\(x \times y=864\\y=864/24\\y=36\\\)

Now ,

The total width of the paper

\(= 24+12\\=36 cm.\)

And , total height of the paper

\(=36+18\\=54 cm.\)

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The incorrect statement is:

B. The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x < 6.

In the given statement, there is an error in the inequality. The correct statement should be:

The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6.

When solving the three-part inequality - 5x < 15x^2 < 3, we need to split it into two separate inequalities. The correct splitting should be:

- 5x < 15x^2 and 15x^2 < 3

Simplifying the first inequality:

- 5x < 15x^2

Dividing by x (assuming x ≠ 0), we need to reverse the inequality sign:

- 5 < 15x

Simplifying the second inequality:

15x^2 < 3

Dividing by 15, we get:

x^2 < 1/5

Taking the square root (assuming x ≥ 0), we have two cases:

x < 1/√5 and -x < 1/√5

Combining these inequalities, we get:

- 5 < 15x and x < 1/√5 and -x < 1/√5

Therefore, the correct statement is that the three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6, not - 6 ≤ 5 - x < 6 as stated in option B.

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Complete question :

shopkeeper sells one machine for 990 re at a profit of 10% and another machine for 1960 at a loss of 2%. What is his gain or loss percent

Answer:

1.72%

Step-by-step explanation:

Given that :

MACHINE 1:

Sales price = 990

Profit percent = 10%

The cost price of the machine (x) :

10% profit of x :

(100 + 10)% of x = 990

110% of x = 990

1.1x = 990

x = 990/1.1

x = 900

MACHINE 2:

Sales price = 1960

Loss on sale = 2%

Cost price (x) :

(100 - 2)% of x = 1960

98% x = 1960

0.98x = 1960

x = 1960/0.98

x = 2000

Total amount realized from sale = (990 + 1960) = 2950

Total cost of production = (2000 + 900) = 2900

Profit Made = (2950 - 2900) = 50

% profit:

(Profit / cost of production) * 100

(50 / 2900) * 100%

0.0172413 * 100%

profit % = 1.72

The profit made is 50

Cost price of first machine will be:

= 100/(100 + 10) × 990

= 100/110 × 990

= 100 × 9

= 900

Cost price for second machine will be:

= (100 - 2) × x = 1960

= 98% × x = 1960

= 0.98x = 1960

x = 1960/0.98.

x = 2000

The total cost price = 900 + 2000 = 2900

Total selling price = 990 + 1960 = 2950

Therefore, profit will be:

= Selling price - Cost price .

= 2950 - 2900

= 50

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According to the quantity theory of money, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply.Velocity can change over time, and changes in velocity may be caused by various factors.

For example, changes in velocity can be caused by shifts in payment practices, changes in the use of credit, changes in the availability of bank deposits or cash, or shifts in demand patterns.Changes in velocity may be related to changes in the money supply.

For example, if the money supply increases, the demand for money may increase, causing the velocity of money to decrease. Conversely, if the money supply decreases, the demand for money may decrease, causing the velocity of money to increase.

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Answer:

87.5%

Step-by-step explanation:

Given:

Area of triangle NCM

⇒ 1/2 × base × height

⇒ 1/2 × CN × CM

⇒ 1/2 × 5 × 4

⇒ 10cm²

Length of rectangle ⇒ 10

Breadth of the rectangle ⇒ 8

↓

Area of rectangle ⇒ Length × Breadth

Area of rectangle ⇒ 10 × 8 = 80cm²

Area of shaded region ⇒ Area of rectangle  -  Area of triangle

Area of shaded region ⇒ 80 - 10 = 80cm²

Percentage of the shaded region = Shaded/complete rectangle × 100

⇒ 70/80 × 100 = 87.5

⇒ The percent of the area of the rectangle shaded is therefore 87.5%.

Answer:

\(P(HH\ u\ C) = \frac{13}{16}\)

Step-by-step explanation:

Given

The Venn diagram

Required

\(P(HH\ u\ C)\)

This is calculated as:

\(P(HH\ u\ C) = \frac{n(HH\ u\ C)}{n(U)}\)

Where:

\(n(U) = 16\) --- count of students

\(n(HH\ u\ C) =13\)

So, we have:

\(P(HH\ u\ C) = \frac{n(HH\ u\ C)}{n(U)}\)

\(P(HH\ u\ C) = \frac{13}{16}\)

Answer:

x = 145

Step-by-step explanation:

x and 35° lie on a straight line and are supplementary angles , sum to 180°

x + 35 = 180 ( subtract 35 from both sides )

x = 145

Using the t-distribution, it is found that since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that Battery B outlasts Battery A by more than 2 hours.

At the null hypothesis, it is tested if it does not outlast by more than 2 hours, that is, the subtraction is not more than 2:

\(H_0: \mu_B - mu_A \leq 2\)

At the alternative hypothesis, it is tested if it outlasts by more than 2 hours, that is:

\(H_1: \mu_B - \mu_A > 2\)

Hence, the standard errors are:

\(s_{Ea} = S_{Eb} = \frac{0.67}{\sqrt{12}} = 0.1934\)

The distribution of the difference has mean and standard deviation given by:

\(\overline{x} = \mu_B - \mu_A = 11.23 - 8.65 = 2.58\)

\(s = \sqrt{s_{Ea}^2 + s_{Eb}^2} = \sqrt{0.1934^2 + 0.1934^2} = 0.2735\)

The test statistic is given by:

\(t = \frac{\overline{x} - \mu}{s}\)

In which \(\mu = 2\) is the value tested at the hypothesis.

Hence:

\(t = \frac{\overline{x} - \mu}{s}\)

\(t = \frac{2.58 - 2}{0.2735}\)

\(t = 2.12\)

The critical value for a right-tailed test, as we are testing if the subtraction is greater than a value, with a 0.05 significance level and 12 + 12 - 2 = 22 df is given by \(t^{\ast} = 1.71\)

Since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that Battery B outlasts Battery A by more than 2 hours.

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Answer:

Step-by-step explanation:

First, let us substitute x and y values: -7 = -2(-5) + 4

Next, let us simplify using the substitution property of equality: 14 = -7 (SEE BELOW MORE INFO).

Now, this does not make sense yet because 14 cannot possibly equal -7. Therefore, we must add a b value, therefore leading us to the equation:

14 + b = -7

by simplifying, we can conclude that b = -21

Finally, we can plug in the b-value into our original equation:

y = -2x + 4 - 21

After simplifying, we get y = -2x - 17. When this is graphed, we can see that -2x - 17 intersects (-5, -7).

Answer:

48%

Step-by-step explanation:

$1200 divided by %25 = 48%

Answer:

It's B

Step-by-step explanation:

Answer:

B is a functional answer

Ab=3.14xRadious to the power of 2

then to the area of the rectange you do B x H = YOUR ANSWER

The function g(x) = x² + 4x has a: A. minimum.

The minimum value occur at x = -2.

The function's minimum value is -4.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function g(x) = x² + 4x, we have:

a = 1, b = 4, and c = 0

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(4)/2(1)

Axis of symmetry, Xmax = -2

Next, we would determine vertex as follows;

g(x) = x² + 4x

g(-2) = -(-2)² + 4(-2)

g(-2) = -4.

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Answer:

its c

Step-by-step explanation:

i think

Answer:

Step-by-step explanation:

45

Answer:

Step-by-step explanation:

5

Answer:

2

Step-by-step explanation:

Convert them to mixed fractions and then find the lcd.

Hope this helps.

Answer:

We need the length to answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

Jdshdcjecjjwdjwddhwedhwedwedwehwdhw?

i think?

Answer:

4

Step-by-step explanation:

substitute the values from the set into the inequality and check validity.

x = 1

5(1)² > 12(1) + 9

5(1) > 12 + 9

5 > 21 ← False

x = 2

5(2)² > 12(2) + 9

5(4) > 24 + 9

20 > 33 ← False

x = 3

5(3)² > 12(3) + 9

5(9) > 36 + 9

45 > 45 ← False

x = 4

5(4)² > 12(4) + 9

5(16) > 48 + 9

80 > 57 ← True

thus the value 4 from the set makes the inequality true

The surface area of the given sphere is 764.15 square inches.

Given that, the sphere has diameter = 15.6 inches.

Here, radius = 15.6/2 = 7.8 inches

We know that, surface area of a sphere is 4πr².

Now, surface area = 4×3.14×7.8²

= 764.15 square inches

Therefore, the surface area of the given sphere is 764.15 square inches.

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The scatter plot shows a [positive linear] association.

From the question, we have the following parameters that can be used in our computation:

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be on a straight line

Also, we can see that

As the x values increases the y values increases

This represents a positive linear association.

Hence, the association is a positive linear association.

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Answer:

2

Step-by-step explanation:

2*3+3*4 x 1/3 power 2

6+12 x 1/9

18 x 1/9

2 x 1 (because 9 and 18 are cutted by each other)

2

2

To evaluate the expression (2b+3a)×(c^2) when a=4, b=3, and c=1/3, we substitute the given values into the expression and perform the indicated arithmetic operations:

(2b + 3a) × (c^2)

= (2(3) + 3(4)) × ((1/3)^2) (substitute a=4, b=3, c=1/3)

= (6 + 12) × (1/9) (evaluate 2(3) + 3(4) and (1/3)^2)

= 18/9

= 2

Therefore, when a=4, b=3, and c=1/3, the expression (2b+3a)×(c^2) equals 2.

Answer:

Step-by-step explanation:

Temperature is a function of the time of day. There can be only one temperature at any particular time.

In contrast, a particular temperature can occur more than one time in a day, so time is not a function of temperature.

Answer:

ab = 1

Step-by-step explanation:

A Reciprocal of a number is a number which when multiplied by the original number yields the multiplicative number, 1.

So the reciprocal of x would be x⁻¹ or ¹⁄ₓ

The information we are given states that the sum of the two non-zero numbers a and b equals the sum of their reciprocals.

So we can write this into an equation and solve,

(See image)

Once we solve, we get the equation (ab-1)(a+b) = 0

We are given info that a+b≠0

So for the above equation to be true, ab-1 has to equal 0

For this to be true, the product ab must equal 1