If the temperature goes down by 7 degrees Celsius when a cold front comes in, how much did it drop on the Fahrenheit scale?

The equation of the parabolas are

y = (x - 2)(x + 2)

y = (x - 2)(x + 2) -4

The graph is attached below.

What is a coordinate grid?

Two parallel lines, known as axes (pronounced AX-eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis. The origin is the location where the x- and y-axes intersect.

Assume the x-intercepts are 2 and -2.

The equation of a parabola whose x-intercepts a and b is y = (x-a)(x-b)

The equation of a parabola is

y = (x-2)(x-(-2))

y = x² - 4 .....(i)

The vertex of the parabola is (0,4).

The parabola's maximum or minimum value is the vertex's y-coordinate.

Thus replace - 4 with -8 of equation (i)

y = x² - 8

Puttin x = 0 in equations (i) and (ii)

y(0) = -4

y(0) = -8

Puttin x = 1 in equations (i) and (ii)

y(1) = -3

y(1) = -7

Puttin x = -1 in equations (i) and (ii)

y(-1) = -3

y(-1) = -7

The points on y = x² - 4 are (0,-4), (1,-3), and (-1,-3).

The points on y = x² - 8 are (0,-8), (1,-7), and (-1,-7).

Plot the points and join them.  

To learn more about maximum or minimum value, click on the below:

https://brainly.com/question/29292066

#SPJ1

Six categories of integers based on their ones digit are:

The cases when sum or difference of the pair is divisible by 10:

Therefore, no matter which seven integers we choose, there is always a pair that meets the condition.

Learn more about Prove Pair Sum/Diff Multiple of 10 here:

https://brainly.com/question/14280621

#SPJ4

The degrees of freedom equals 7.

The test statistic will be 2.55

The critical value will be 1.89.

From the information, they randomly sample 20 individuals and administer a 30 item true or false psychological test designed to measure depression and the scores that are greater than 20 indicate significant levels of depression.

The degree of freedom will be:

= n - 1

= 8 - 1

= 7

The test statistic will be:

= 22.25 - 20 /2.49 ✓8

= 2.55

The critical value will be 1.89.

Based on the information, it should be noted that we will fail to reject the null hypothesis.

Learn more about experiments on

brainly.com/question/17274244

#SPJ1

Answer:

let the two numbers be x and y.

Given ,

[tex] \underline{\underline{\frac{x}{y} = \frac{3}{5}}} \\ [/tex]

To find - ratio of squares of the two numbers.

[tex]\longrightarrow \: \frac{ {x}^{2} }{ {y}^{2} } = ( \frac{ {3}^{2} }{ {5}^{2} } ) \\ \\ \longrightarrow \: \boxed{\frac{ {x}^{2} }{ {y}^{2} } = \frac{9}{25} }[/tex]

Therefore ,

[tex] \underline{\underline{ratio \: of \: the \: squares \: of \: two \: numbers \: = \: 9 \: : \: 25}} [/tex]

hope helpful! :)

Answer:

hxxu u uu u. yy h gghchcvhhvuvuvuvuvhcuchchcjvj jvjcjcjcchhchcjcjc

Step-by-step explanation:

g g g g g. gg g

After solving the value of E(x^2 + 3) is 11.7.

The distribution of x is:

x            f(x)              x^2             x^2·f(x)

1             0.2               1                    0.2

2            0.3               4                    1.2

3             0.1               9                    0.9

4             0.4              16                   6.4

We have to determine the value of E(x^2 + 3).

We can write it as

E(x^2 + 3) = E(x^2) + 3...........(1)

As E(x^2) = Sum of x^2·f(x)

E(x^2) = 0.2 + 1.2 + 0.9 + 6.4

E(x^2) = 8.7

Now putting the value of E(x^2) in equation 1, we get

E(x^2 + 3) = 8.7 + 3

E(x^2 + 3) = 11.7

To learn more about distribution of x link is here

brainly.com/question/30437411

#SPJ4

The complete question is:

Let x have the following distribution:

x            1         2         3         4

f(x)        0.2     0.3      0.1      0.4

Find E(x^2 + 3) (write it up to first decimal place).

The exponential function r=(0.88)^4t can be written as r=(1-0.12)^4t.

What are exponential functions?

An exponential function is a Mathematical function in the form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Now,

given exponential function is r(r) = (0.88)^4t

we can rewrite its as  r=(1-0.12)^4t. to find whether it is increasing or decaying. As the - sign shows decrement.

hence,

             Given exponential function is decaying in nature..

To know more about exponential function visit the link

https://brainly.com/question/14355665?referrer=searchResults

#SPJ1

The predicted egg production in 2001 is given as follows:

65.6 billion.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The production in 1995 was of 52.7, hence the intercept b is given as follows:

b = 52.7.

In 4 years, the production increased to 61.3, hence the slope m is given as follows:

m = (61.3 - 52.7)/4

m = 2.15.

Hence the function is of:

y = 2.15x + 52.7.

2001 is 6 years,hence the estimate is given as follows:

y = 2.15(6) + 52.7

y = 65.6 billion.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

The value of given expression 7 raised to the power 2 divided by 7 raised to the power 3 is 1 / 7

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Given expression,

7 raised to the power 2 divided by 7 raised to the power 3

7 ^ 2 / 7 ^ 3

The value of a ^ m / a ^ n  = a ^ m-n

= 7 ^ (2-3)

= 7 ^ ( -1)

= 1 / 7 .

Therefore, The value of given expression 7 raised to the power 2 divided by 7 raised to the power 3 is 1 / 7

To learn more about Algebraic expression from given link.

https://brainly.com/question/953809

#SPJ1

The new length of the longer side after application of a scale factor of 1/4 is; 7.125 ft

A scale factor is defined as the ratio between the scale of a given original object and a new object. This will be indicative of its' representation but of a different size. Thus, it could represent an enlargement or a reduction.

Now, we are given that the length of the sides are;

Length of longer sides = 28.5 cm

Length of shorter side = 16.5 cm

Thus, if the scale factor is 1/4, then it means that;

New length of longer side = 1/4 * 28.5

New length = 7.125 ft

Read more about Scale Factors at; https://brainly.com/question/10253650

#SPJ1

The value of y is 1446.38.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

y = 601 [tex](1.05)^{18}[/tex]

Now,

y = 601 x 2.4066192336911

y = 1446.3781

y = 1446.38

Thus,

y = 1446.38

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Answer:

92

Step-by-step explanation:

We first do 12x7 which equals to 84

Then we add 8 which equals to 92

The number of ordered pairs $(x,y)$ of positive integers that satisfy the equation would be 480.

We only count one ordered pair by substituting 2 for 60 in this case. We count four ordered pairs by doing with 4.

We got 7 pairings from 6 people. I add 8 to get 12, thus. the difference between neighboring phrases by moving on and doing so (1,3,3,5,5,...).

We believe that if 2n were substituted for 60, we would find 1+3+3+5+5+7+7.... where n words will be present.

So, 1+3+3+5+5... 29+29+31 = 16*30 = 480 is our response.

The number of ordered pairs $(x,y)$ of positive integers that satisfy the equation would be 480.

Know more about positive integers

https://brainly.com/question/1367050

#SPJ4

The full question:

Find the number of ordered pairs $(x,y)$ of positive integers that satisfy the following equation

The exact values of each trigonometric function are 4/5, 3/5, 4/3, 5/4, 5/3, and 3/4.

Given, the terminal side of contains the point p(9, 12).

Each trigonometric function must have an exact value, which we must determine.

A line segment drawn from the origin to the point should have a length of r.

r = √x2 + y2

Here, x = 9 and y = 12

r = √(9)2 + (12)2

= √81 + 144

= √225

r = 15

sin θ = y/r = 12/15 = 4/5

cos θ =x/r = 9/15 = 3/5

tan θ = y/x = 12/9 = 4/3

cosec θ = 1/sin θ = 5/4

sec θ = 1/cos θ = 5/3

cot θ = 1/tan θ = 3/4

Consequently, each trigonometric function's precise values are 4/5, 3/5, 4/3, 5/4, 5/3, and 3/4.

Know more about trigonometric function

https://brainly.com/question/25618616

#SPJ4

The full question:

The point p(9, 12) is on the terminal side of θ. Find the exact values of each trigonometric function.

Answer:

[tex]y = 10.5[/tex]

Step-by-step explanation:

[tex]\frac{5}{4} y = 13\\[/tex]

We transpose

[tex]y =\frac{13X4}{5}[/tex]

[tex]y = \frac{52}{5}[/tex]

[tex]y = 10.5[/tex]

The area of the rectangular garden can be calculated as follows: 57 m * 42 m = 2406 m^2.

The ornamental fence with a width of 60 cm has a width of 0.6 m. If the fence is planted inside the perimeter of the garden, the length of the garden will decrease by 2 * 0.6 m = 1.2 m and the width of the garden will decrease by 2 * 0.6 m = 1.2 m.

So, the new length and width of the garden will be 57 m - 1.2 m = 55.8 m and 42 m - 1.2 m = 40.8 m, respectively.

The new area of the garden can be calculated as follows: 55.8 m * 40.8 m = 2270.784 m^2.

Finally, the decrease in area can be calculated as follows: 2406 m^2 - 2270.784 m^2 = 35.216 m^2.

Therefore, the area of the garden will decrease by 35.216 m^2.

Answer:

The width of the ornamental fence is 60 cm, which is equal to 60/100 = 0.6 meters.

The total length of the ornamental fence that will be planted inside the perimeter of the rectangular garden is 2 * (57 m + 42 m) = 2 * 99 m = 198 m.

The decrease in the area of the garden due to the ornamental fence is 0.6 m * 198 m = 118.8 m^2.

The rule shows the input and output of the reflection is, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.

And, The new coordinate of A' = (- 5, - 1)

Reflection is a type of transformation that flip a shape in mirror line, so that each point is the same distance from the mirror line as its reflected point.

We have to given that;

Parallelogram ABCD is shown. A is at (-5, 1), B is at (-4, 3). C is at (-1, 3) . D is at (-2, 1).

We know that;

When a point is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.

And, The reflection of point (x, y) across the x-axis is (x, -y).

Hence, The new coordinate of A' is,

⇒ (- 5, 1) = (- 5, - 1)

Learn more about the reflection visit:

https://brainly.com/question/26494295

#SPJ1

The union of two subspaces of V is a subspace of V if and only if one of the subspaces of v is contained in the other

Let [tex]$V_1, V_2$[/tex] be the two subspaces of V. Suppose [tex]$V_1 \cup V_2$[/tex] is a subspace of V.

Then if [tex]$x_1 \in V_1$[/tex] and [tex]$x_2 \in V_2$[/tex] then we must have [tex]$x_1 \in V_1 \cup V_2$[/tex] and[tex]$x_2 \in V_1 \cup V_2$[/tex] so that we must have [tex]$x_1+x_2 \in V_1 \cup V_2$[/tex].

If and only if one of the subspaces is contained in the other, the union of the two subspaces is a subspace.

But this by definition means [tex]$x_1+x_2 \in V_1$[/tex] or [tex]$x_1+x_2 \in V_2$[/tex]. Either way, by the existence of additive inverses and the closure properties for the subspaces we have:

[tex]\left(x_1+x_2\right)+\left(-x_1\right) \in V_1[/tex]

Or

[tex]\left(x_1+x_2\right)+\left(-x_2\right) \in V_2[/tex]

By the associative/commutative properties, we have:

[tex]x_2 \in V_1 \text {, or, } x_2 \in V_1[/tex]

Thus we have shown if [tex]$x_1 \in V_1$[/tex] and [tex]$x_2 \in V_2$[/tex] then [tex]$x_1 \in V_2$[/tex] or [tex]$x_2 \in V_1$[/tex]. If [tex]$x_1 \in V_2$[/tex] for all [tex]$x_1 \in V_1$[/tex] then we have [tex]$V_1 \subseteq V_2$[/tex]. If [tex]$x_2 \in V_1$[/tex] for all [tex]$x_2 \in V_2$[/tex] then [tex]$V_2 \subseteq V_1$[/tex]. In either case, we see one subspace is a subset of the other.

For more questions on subspaces

https://brainly.com/question/14992310

#SPJ4

53 is the value of the 99% of the time.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range, while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center

Given, Let X represent the lifetime in months of a battery, and someone claims that X~N(50,25). We wish to investigate the claim, so 16 batteries are life-tested and the average survival times of the 16 batteries are Comput.

μ = 50

σ² = 25

n = 16

So, the Population standard deviation

σ² = 25

σ = 5

To find the value 99% of the time

The z-score will be

P(z <Z) = 0.999

P(z < 2.326) = 0.999

Z = 2.326

To find a z score corresponding to a known probability, select fx, Statistical, NORMSINV, and enter the total area to the left of the given value.

Now we determine the z-score using the z-score formula

x = μ + (Z *σ  / √n)

x = 53

Therefore, the value of 99% of the time is 53.

Learn more about normal distribution here:

https://brainly.com/question/29509087

#SPJ1

Complete question:

The account balance when they retire is $13,221.96

The formula for compound interest is:

A = P (1 + r/n)^(nt)

where:

A = the future value of the investment/loan, including interest

P = the principal investment/loan amount

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years the money is invested/borrowed for

A is the account balance when they retire

P = $7,500, r = 3.2% = 0.032, n = 1, t = 58-40 = 18 years

A = P (1 + r/n)^(nt)

A = 7,500(1 + 0.032/1)^(1*18)

A = 7,500(1 .032)¹⁸

A = $13,221.96

Learn more about compound interest on:

brainly.com/question/24274034

#SPJ1

Expected value of the mean = 50 (the population mean)

The expected value of the mean for a sample size of 4 from a population with a mean of 50 and a standard deviation of 12 can be calculated using the central limit theorem.

According to the central limit theorem, the expected value of the mean of a sample from a population approaches the population mean as the sample size increases. In other words, as the sample size becomes larger, the sample mean becomes a more accurate estimate of the population mean.

In this case, the expected value of the mean of a sample of 4 from a population with a mean of 50 and a standard deviation of 12 can be calculated as follows:

Expected value of the mean = 50 (the population mean)

It is important to note that the expected value of the mean is equal to the population mean, regardless of the sample size. The central limit theorem states that the sample mean approaches the population mean as the sample size increases, but for a sample size of 4, the expected value of the mean is still equal to the population mean.

Learn more about Mean Median Mode here:

brainly.com/question/4001516

#SPJ1

Answer:

[tex]y \: = 2cos \: ( \frac{\pi}{5} x) - 3[/tex]

The length of the unknown side or, the length of AC = 22.62.

To calculate the length of the unknown side in a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides or, in familiar algebraic notation, a2 + b2 = c2.

In this Question, side AC is the hypotenuse, so we can use the Pythagorean theorem to find the length of side AC:

AC^2 = AB^2 + BC^2

We know that AB = 12 and BC = 19, so we can substitute these values into the equation:

AC^2 = 12^2 + 19^2

AC^2 = 144 + 361

AC^2 = 505

To find the length of AC, we can take the square root of 505:

AC = √505

Rounded to two decimal places, the length of AC = 22.62.

Learn more about the Pythagorean theorem,

https://brainly.com/question/343682

Using the ALEKS calculator , 13.1 would roughly equal 172, rounded to the closest hundredth.

When necessary, ALEKS offers a calculator so that users may determine the difference. Instead of using your own calculator, just utilize ALEKS'. For the calculator to produce most accurate assessment results, it must only be used in the manner specified by ALEKS.

Reviewers believed that Khan Academy and ALEKS better satisfy their needs as a business. Reviewers believed that Open Courseware is the best choice when considering the level of continuing product support. Our evaluators liked the approach of Online Courses over ALEKS for feature releases and roadmaps.

To know more about ALEKS Calculator visit :

https://brainly.com/question/29126431

#SPJ1

Mercury, gallium, and caesium often have low melting points, except gold. The only liquid metal with a 38 °C melting temperature is mercury.

They have high melting and boiling points because melting and boiling require a lot of energy to break through the strong metallic connections present in a metal's massive structure.

Brass: 930 °C (1710 °F) Aluminium Bronze*: 1027-1038 °C (1881-1900 °F) Chromium: 1860 °C (3380 °F) Copper: 1084 °C (1983 °F).

In general, aluminium is an easy metal to melt, and it is easy to get your hands on.  To make aluminum metal shapes, many people melt discarded soda cans made of aluminum. The aluminum should be heated until it melts completely.

Therefore, the melting or boiling point will be higher the more energy is required. Varying metals have different melting and boiling points because the force of attraction between the metal ions differs between them.

Learn more about metal here:

https://brainly.com/question/28199316

#SPJ1

This suggests that a gas's pressure decreases as its volume increases. Similar to this, a gas's pressure rises as its volume decreases. The balloon's expansion for the given implies that its volume grows. Boyle's law predicts that its pressure will decrease as a result.

In other words, as the atmospheric gas exerts less pressure on the surface of the balloon, the interior gas expands until the internal and external pressures are equal. This is why weather balloons grow larger as they ascend through the atmosphere to lower pressure regions because the volume of the gas has increased.

You can observe Avogadro's Law whenever you blow up a balloon. By inflating the balloon, you can add moles of gas, which increases the balloon's volume.

To know more about volume visit:-

brainly.com/question/12237641

#SPJ1

Answer:

129

Step-by-step explanation:

516/4 = 129

If this answer helped you, please leave a thanks or a Brainliest!!!

Have a GREAT day!!!

By concept of linear equations, The number of birds is 14 and number of lions is 17.

What is a linear equation ?

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

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Let no. of birds=x and no. of lions=y

Given heads=31

and feet=96

Therefore, the equations will be

             x+y=31 and 2x+4y=96

from given equations x=14 and y=17.

Hence,

           The number of birds is 14 and number of lions is 17.

To know more about linear equations visit the link

https://brainly.com/question/29739212?referrer=searchResults

#SPJ1

The comparison of the fractions are

15/24 < 16/24, 3/18 < 4/18 and 14/24 <15/24

Fraction 1

Here, we have

5/8 and 2/3

The LCM of 8 and 3 is 24

So, the pair is

15/24 and 16/24

When compared, we have

15/24 < 16/24

Fraction 2

Here, we have

1/6 and 2/9

The LCM of 6 and 9 is 18

So, the pair is

3/18 and 4/18

When compared, we have

3/18 < 4/18

Fraction 3

Here, we have

7/12 and 5/8

The LCM of 12 and 8 is 24

So, the pair is

14/24 and 15/24

When compared, we have

14/24 <15/24

Read more about fraction at

https://brainly.com/question/1622425

#SPJ1