A parabola can be drawn given a focus of (5, 10) and a directrix of y= -2. what can be said about the parabola?

the parabola has a vertex at (_,_), has a low-value of _ and it opens __.

Answer:

Step-by-step explanation:

Find the exact frequency table in the diagram attached. x is the midpoint of the interval f is the frequency. Using the formula below to find the mean;

[tex]\overline x = \frac{\sum fx}{\sum f} \\[/tex]

[tex]\sum fx = (42*2)+(47*7)+(52*9)+(57*5)+(62*1)\\\sum fx = 84+329+468+285+62\\\sum fx = 1,228\\\sum f = 24\\\\\overline x = \frac{1,228}{24} \\\overline x = 51.17^{0} F[/tex]

The mean of the frequency distribution compare to the actual mean of 50.7°F is 51.2°F(to nearest tenth)

Answer:

15

Step-by-step explanation:

The pattern is going by 15 because 10+15=25 and then continue going.

Answer:

15 is the answer

Step-by-step explanation:

Answer:I think it -5 wait lemme check answer again

The solution to the inequality will be greater than or equal to –5. Then the correct option is B.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

3(x – 4) ≥ 5x – 2

Simplify the equation, then the solution to inequality will be

3(x – 4) ≥ 5x –2

3x – 12 ≥ 5x –2

5x – 3x ≤ – 12 + 2

2x ≤ – 10

x ≤ –5

The solution to the inequality will be greater than or equal to –5.

Then the correct option is B.

The correct equation is 3(x – 4) ≥ 5x – 2.

More about the inequality link is given below.

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Answer:

The answer is x ≤ 2.

Step-by-step explanation:

Firstly, you have to move the unrelated term to the other side :

[tex] - 9 \leqslant 7 - 8x[/tex]

[tex] - 9 - 7 \leqslant - 8x[/tex]

[tex] - 16 \leqslant - 8x[/tex]

Next you can solve it :

[tex] - 8x \geqslant - 16[/tex]

[tex]x \leqslant - 16 \div - 8[/tex]

[tex]x \leqslant 2[/tex]

*Remember to change the symbol, when it is dividing by a negative value

Answer:

462cm^3

Step-by-step explanation:

Volume of a pyramid = 1/3 × base area × height

Now the base is a rectangle with sides 7cm and 18cm; area of base is;

7 × 18 = 126cm^2

Therefore volume =

1/3 × 126 × 11 = 42 × 11= 462cm^3

Answer:

3

Step-by-step explanation:

6/4 (divide numerator and denominator each by 2)

= 3/2

= 3 x (1/2)

hence there are 3  halves in 6/4

Answer:

3

Step-by-step explanation:

To find out, we need to divide.

[tex]\frac{6}{4}[/tex] ÷ [tex]\frac{1}{2}[/tex]

When dividing fractions, you multiply the 1st term by the second term's reciprocal.

so

[tex]\frac{6}{4}[/tex] x 2

If you simplify you get [tex]\frac{6}{2}[/tex] or 3.

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Tangents that meet at a point are equal in length so DB = CB

Let's form an equation:

10x + 16 = 5x + 20

- 16 from both sides

10x = 5x + 4

- 5x from both sides

5x = 4

/5 on both sides

x = 4/5

Sub this value into the expression for CB

5(4/5) + 20 = 24

Thus, the answer is option D. 24

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Answer:

4TH OPTION

Step-by-step explanation:

IN A CIRCLE , TANGENT DRAWN FROM AN EXTERNAL POINT TO THE CIRCLE ARE EQUAL.

ie BD = BC

ie 10x +16 = 5x+20

10x - 5x = 20 -16

5x = 4

x = 4/5

therfore BC = 5x+20 = 5*4/5 +20

BC= 4+20

BC = 24

HOPE IT HELPS...

Answer:

The mean and standard deviation of the corrected pH measurements are 6.63 and 3.8025 respectively.

Step-by-step explanation:

We can correct the values of the mean and standard deviation using the properties of the mean and the variance.

To the original value X we have to add 0.2 and multiply then by 1.3 to calculate the new and corrected value Y:

[tex]Y=1.3(X+0.2)[/tex]

The mean and standard deviation of the original value X are 4.9 and 1.5 respectively.

Then, we can apply the properties of the mean as:

[tex]E(Y)=E(1.3(X+0.2))=1.3E(X+0.2)=1.3E(X)+1.3*0.2\\\\E(Y)=1.3E(X)+0.26\\\\E(Y)=1.3*4.9+0.26=6.37+0.26=6.63[/tex]

For the standard deviation, we apply the properties of variance:

[tex]V(Y)=V(1.3(X+0.2))\\\\V(Y)=1.3^2\cdot V(X+0.2)\\\\V(Y)=1.69\cdot V(X)\\\\V(Y)=1.69\cdot 1.5^2=1.69\cdot 2.25=3.8025[/tex]

The properties that have been applied are:

[tex]1.\,E(aX)=aE(X)\\\\ 2.\,E(X+b)=E(X)+b\\\\3.\,V(aX)=a^2V(X)\\\\4.\,V(X+b)=V(X)+0[/tex]

Answer:

11

Step-by-step explanation:

I looked it up for you so no problem

Answer: 11 and 22

Step-by-step explanation:

We can start by making an equation. Since we know we have two numbers added to make 33. One number can be represented by x and the other is half of this x number so we can write this equation.

33 = 1/2x + x

Now we can combine like terms.

33 = 3/2x

Then either multiply by the reciprocal or divide by 1.5 on both sides.

x = 22

And the other number is half this number so divide by 2.

y = 11

Answer:

H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]

H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]

The statistic would be given by:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{10}{8}=1.25[/tex]

Step-by-step explanation:

Information given

[tex]n_1 = 60 [/tex] represent the sample size 1

[tex]n_2 =40[/tex] represent the sample size 2

[tex]s^2_1 = 8[/tex] represent the sample variance 1

[tex]s^2_2 = 10[/tex] represent the sample variance 2

The statistic to check the hypothesis is given by:

[tex]F=\frac{s^2_2}{s^2_1}[/tex]

Hypothesis to test

We want to test if the two variances are equal, so the system of hypothesis are:

H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]

H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]

The statistic would be given by:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{10}{8}=1.25[/tex]

Answer:

6, -6, 6, -6 and 6.

Step-by-step explanation:

Given the recursion formula for a sequence

[tex]a_{n+1}=-a_n\\$where a_1=6\\[/tex]

The first five terms of the sequence are:

[tex]\text{First Term, }a_1=6\\$Second Term, a_2=a_{1+1}=-a_1=-6\\$Third term, a_3=a_{2+1}=-a_2=6\\$Fourth term, a_4=a_{3+1}=-a_3=-6\\$Fifth term, a_5=a_{4+1}=-a_4=6[/tex]

Therefore, the first five terms of the sequence:

[tex]a_1,a_2,a_3,a_4,a_5=6, -6, 6, -6$ and 6.[/tex]

Answer:

The experimental probability that the next contestant will qualify for the bonus round is [tex]\frac{7}{10}[/tex]

Step-by-step explanation:

The experimental probability of an outcome is the number of trials in which the desired outcome happened divided by the total number of trials.

What is the experimental probability that the next contestant will qualify for the bonus round?

14 contestants qualified out of 14+6 = 20 contestants. So

[tex]p = \frac{14}{20} = \frac{7}{10}[/tex]

The experimental probability that the next contestant will qualify for the bonus round is [tex]\frac{7}{10}[/tex]

Answer:

B. [[0,4]

   [-6,1]

  [3,-4]]

Step-by-step explanation:

If you multiply the matrices, you get the answer.

Answer:

[tex] E(X) = 7*0.18 +9*0.08 +11*0.09 +15*0.08 +17*0.41 =13.22[/tex]

And we can find the second moment with this formula:

[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]

And replacing we got:

[tex] E(X^2) = 7^2*0.18 +9^2*0.08 +11^2*0.09 +15^2*0.08 +17^2*0.41 =189.72[/tex]

And we can find the variance like this:

[tex] Var(X) = E(X^2) -[E(X)]^2= 189.72- (13.22)^2 =14.9516[/tex]

And the deviation would be:

[tex] Sd(X)= \sqrt{14.9516}= 3.867[/tex]

Step-by-step explanation:

For this case we have the following dataset given:

Payment     $7     $9     $11    $13    $15  $17

Probability 0.18  0.08  0.09  0.16  0.08   0.41

For this case we can calculate the mean with this formula:

[tex] E(X) = \sum_{i=1}^n X_i P(X_i)[/tex]

And replacing we got:

[tex] E(X) = 7*0.18 +9*0.08 +11*0.09 +15*0.08 +17*0.41 =13.22[/tex]

And we can find the second moment with this formula:

[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]

And replacing we got:

[tex] E(X^2) = 7^2*0.18 +9^2*0.08 +11^2*0.09 +15^2*0.08 +17^2*0.41 =189.72[/tex]

And we can find the variance like this:

[tex] Var(X) = E(X^2) -[E(X)]^2= 189.72- (13.22)^2 =14.9516[/tex]

And the deviation would be:

[tex] Sd(X)= \sqrt{14.9516}= 3.867[/tex]

Answer:

0.9 grams

Step-by-step explanation:

The point estimate for the average weight of Soap Bar A is:

[tex]A=\frac{121+122+124+ 123+ 120+ 124+ 121+ 121+ 121+ 123+ 120}{11}\\A=121.82\ grams[/tex]

The point estimate for the average weight of Soap Bar B is:

[tex]B=\frac{121+120+122+ 119+ 121+ 122+ 122+ 120+ 120 +121+ 122+123+119}{13}\\B=120.92\ grams[/tex]

Therefore, the point estimate for the true difference between the given population means is:

[tex]Dif = A-B\\Dif = 121.82-120.92\\Dif=0.9\ grams[/tex]

The point estimate for the difference is 0.9 grams.

Answer:

The answer is true

Step-by-step explanation:

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2

Answer:

 A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, negative 1.5, 1.5, 3, 4.5.

Step-by-step explanation:

When the x-values are evenly spaced, a linear function will have evenly-space y-values.

In the first table, the y-differences are all +8.

In the second table, the y-differences are 0, 1.5, 1.5, so are not all the same.

In the third table, the y-differences are all -3.

The second table represents a non-linear function.

__

In the graph, you can see that the points from the second table (purple) are not on a straight line.

Answer:

B

Step-by-step explanation:

Answer:

The low tide, when it is 10 feet below the high tide would be at 7am and 7pm

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

Basically the ratio was multiplied by 12 to get the number of boys so you do the same to the other one.

Answer:

number of boys+number of girls=48boys+36girls=84members

Step-by-step explanation:

FIRST WE FIND THE NUMBER OF GIRLS BY STATISTICAL METHOD

4:3=48:x

4/3=48/x

By cross multiplication

4×x=48×3

4x=144

Dividing 4 on both sides

4x/4=144/4

x=36=number of girls

Yes, B. Rising action is correct

Answer:

2,322,775

Step-by-step explanation:

Given a1 = 4 and ai =ai-1 +11

when i = 2

a2 = a2-1+11

a2 = a1+11

a2 = 4+11

a2 = 15

when i = 3

a3 = a2+11

a3 = 15+11

a3 = 26

The sequence formed by a1, a2, a3... is am arithmetic sequence as shown;

4, 15, 26...

Sum of nth term of an arithmetic sequence = n/2{2a+(n-1)d}

a is the first term = 4

d is the common difference = 15-4 = 26-15 = 11

n is the number of terms.

Since we are to find the sum of the first 650 terms in the sequence, n = 650

S650 = 650/2{2(4)+(650-1)11}

S650 = 325{8+(649)11}

S650 = 325(8+7,139)

S650 = 325×7147

S650 = 2,322,775

Answer:

The answer is D.

Step-by-step explanation:

First, you have to convert the mixed number into improper fraction :

[tex]6 \frac{2}{3} [/tex]

[tex] = \frac{3 \times 6 + 2}{3} [/tex]

[tex] = \frac{20}{3} [/tex]

Next, you can divide it by cutting out the common factor :

[tex]15 \div \frac{20}{3} [/tex]

[tex] = 15 \times \frac{3}{20} [/tex]

[tex] = 3 \times \frac{3}{4} [/tex]

[tex] = \frac{9}{4} [/tex]

[tex] = 2 \frac{1}{4} [/tex]

The value of the expression after divide is,

⇒ 2 1/4

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒ 15 divided by 6 2/3

Now,

We can divide as;

⇒ 15 divided by 6 2/3

⇒ 15 ÷ 6 2/3

⇒ 15 ÷ 20/3

⇒ 15 × 3/20

⇒ 45/20

⇒ 9/4

⇒ 2 1/4

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Answer:

two to the thrid power is 8.

Step-by-step explanation:

2^3= 8

Answer:

I'm not sure what exactly the question is but it should be 8

Step-by-step explanation:

2^3

2×2×2=8

Answer: c

Step-by-step explanation: 4/1 x 1/3 = 4/3

Answer:

a) Particle has a constant speed of 4, b) Velocity and acceleration vector are orthogonal to each other, c) Clockwise, d) False, the particle begin at the point (0,1).

Step-by-step explanation:

a) Let is find first the velocity vector by differentiation:

[tex]\vec v = \frac{dr_{x}}{dt} i + \frac {dr_{y}}{dt} j[/tex]

[tex]\vec v = 4\cdot \cos 4t\, i - 4 \cdot \sin 4t \,j[/tex]

[tex]\vec v = 4 \cdot (\cos 4t \, i - \sin 4t\,j)[/tex]

Where the resultant vector is the product of a unit vector and magnitude of the velocity vector (speed). Velocity vector has a constant speed only if magnitude of unit vector is constant in time. That is:

[tex]\|\vec u \| = 1[/tex]

Then,

[tex]\| \vec u \| = \sqrt{\cos^{2} 4t + \sin^{2}4t }[/tex]

[tex]\| \vec u \| = \sqrt{1}[/tex]

[tex]\|\vec u \| = 1[/tex]

Hence, the particle has a constant speed of 4.

b) The acceleration vector is obtained by deriving the velocity vector.

[tex]\vec a = \frac{dv_{x}}{dt} i + \frac {dv_{y}}{dt} j[/tex]

[tex]\vec a = 16\cdot (-\sin 4t \,i -\cos 4t \,j)[/tex]

Velocity and acceleration are orthogonal to each other only if [tex]\vec v \bullet \vec a = 0[/tex]. Then,

[tex]\vec v \bullet \vec a = 64 \cdot (\cos 4t)\cdot (-\sin 4t) + 64 \cdot (-\sin 4t) \cdot (-\cos 4t)[/tex]

[tex]\vec v \bullet \vec a = -64\cdot \sin 4t\cdot \cos 4t + 64 \cdot \sin 4t \cdot \cos 4t[/tex]

[tex]\vec v \bullet \vec a = 0[/tex]

Which demonstrates the orthogonality between velocity and acceleration vectors.

c) The particle is rotating clockwise as right-hand rule is applied to model vectors in 2 and 3 dimensions, which are associated with positive angles for position vector. That is: [tex]t \geq 0[/tex]

And cosine decrease and sine increase inasmuch as t becomes bigger.

d) Let evaluate the vector in [tex]t = 0[/tex].

[tex]r(0) = \sin (4\cdot 0) \,i + \cos (4\cdot 0)\,j[/tex]

[tex]r(0) = 0\,i + 1 \,j[/tex]

False, the particle begin at the point (0,1).

Answer:

2.555555

Step-by-step explanation: Nine times 2 is 18. When we subtract 18 from 23 we get 5. In the quotient we add a decimal point and add a zero to 5 which is 50. Nine times 5 is 45. When we subtract 45 from 50 we get 5 again and again and again . In decimal form it is 2.5555555.

Answer:

2.55 Hope this helps!

Answer:

As you know, a year has around 365 + 1/4 days.

This means that in two years, we have:

365 + 356 + 1/4 + 1/4 = 730 + 1/2

and so on.

adding this up, when we have 4 years we have a full day extra, this is:

1460 + 1

When we divide 1461 by 4, we have 365 with a surpass of 1.

The rule used to keep the calendar in sync with this extra day is adding an extra day to each fourth year.

So each fourth year, we have an extra day in Februray (the Februray 29th), this is called a bisiest year.

The "math rule" used to know if a year is leap or not is:

if a year is not divisible by 4, then it is a common year

else if the year is not divisible by 100 then it is a leap year,

else if the year is not divisible by 400, then it is a common year

if not, the year is a leap year.

Where "year" represents the number of the year.

Answer:

[tex] \frac{19}{20} [/tex]

Step-by-step explanation:

[tex] \frac{7}{10} + \frac{1}{4} \\ \frac{14 + 5}{20} \\ = \frac{19}{20} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

The horizontal distance from the center is 49.3883 feet

Step-by-step explanation:

The equation of an ellipse is equal to:

[tex]\frac{x^2}{a^{2} } +\frac{y^2}{b^{2} } =1[/tex]

Where a is the half of the wide, b is the high of the ellipse, x is the horizontal distance from the center and y is the height of the ellipse at that distance.

Then, replacing a by 106/2 and b by 33.9, we get:

[tex]\frac{x^2}{53^{2} } +\frac{y^2}{33.9^{2} } =1\\\frac{x^2}{2809} +\frac{y^2}{1149.21} =1[/tex]

Therefore, the horizontal distances from the center of the arch where the height is equal to 12.3 feet is calculated replacing y by 12.3 and solving for x as:

[tex]\frac{x^2}{2809} +\frac{y^2}{1149.21} =1\\\frac{x^2}{2809} +\frac{12.3^2}{1149.21} =1\\\\\frac{x^2}{2809}=1-\frac{12.3^2}{1149.21}\\\\x^{2} =2809(0.8684)\\x=\sqrt{2809(0.8684)}\\x=49.3883[/tex]

So, the horizontal distance from the center is 49.3883 feet