-2x2 + 1 for x = -3​

Answer:

$43 + $6l

Step-by-step explanation:

Hello!

She spends $43 and bus several $6 laces.

We don't know how many she buys, but we know that we can represent that number using l.

That means she spends $43 + $6l.

The algebraic expression is $43 + $6l.

We can determine the price if we know the number of laces she buys. We can simply plug in the number of laces she bought, and we can plug it in for l in the equation.

Answer:

43= 6(x)

Explanation:

43 is the total,  and each of them are 6$ each. X is the variable that we don't know.

By definition of the volume of cube, the side length of the cubic quart container is approximately equal to 9.818 centimeters.

A quart means a quarter of gallon and is equal to 946.353 cubic centimeters. The volume of the cube is equal to the cube of the side lengt, then:

x³ = 946.353

x = ∛946.353

x ≈ 9.818

By definition of the volume of cube, the side length of the cubic quart container is approximately equal to 9.818 centimeters.

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Answer:

they are proportionate

Step-by-step explanation:

1560/100 = 15.6

312/100 = 3.12

Answer: Because they're based off the power of 10.

Step-by-step explanation:

I think the answer is correct because, to make 15.6 to 1560 you just need to multiply by 100, and to get 3.12 to 312 all you have to do is multiply by 100. So if you divided 1560 and 312 which is 5, all you have to do is divide by 100 and you get the same answer thats why its basically considered the same because of the power of tens.

Hope This Helps!

Answer:

I think strong positive

Step-by-step explanation:

.......

Answer:

yes

Step-by-step explanation:

becuase 12 is 2/3 of 18 and 4 is 2/3 of 6

Answer:

yes they are equivalent because they both get the same answer 0.3

There are 41 ways to distribute five distinguishable objects into three indistinguishable boxes.

The boxes are indistinguishable, there are 5 different ways to arrange the number of balls in each box: (5,0,0), (4,1,0), (3,2,0), (3,1,1), or (2,2,1).

There is 1 way to put all 5 balls in one box i.e (5,0,0)

(4,1,0): There are 5 choices for the 4 balls in one of the boxes.

(3,2,0): There are 10 choices for the 3 balls in the boxes.

(3,1,1): There are 10 choices for the 3 balls in one of the boxes, and we can simply split the last two among the other indistinguishable boxes.

(2,2,1): There are 10 options for one of the boxes with two balls, then 3 options for the second box with two balls, and one for remaining for the third.

Therefore the boxes with two balls are indistinguishable, we are counting each pair of balls twice so we have to divide by two.

So there are (10×3)/2=15 arrangements of balls as (2,2,1).

Hence the total number of arrangements for 3 indistinguishable boxes and 5 distinguishable balls is 1+5+10+10+15=41.

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Answer: Each friend got 3 cookies.

Step-by-step explanation:

Johann gets three cookies so 24-3=21. Divide it by the seven friends that came. 21/7=3 cookies.

Answer:

Step-by-step explanation:

So 7 of his friends came to the party and 3 cookies were left for himself. To find how many cookies each friend got, first subtract the 3 cookies Johann has from the total.

24-3=21

Then divide 21 by the number of friends.

21÷7=3

So each friend got 3 cookies.

Answer:

10: 12 units^2 11: 33 units^2

Step-by-step explanation:

10:

Divide into square and 2 triangles (for simplicity)

square=9

one triangle=3/2

both triangles combined=3

9+3=12

11:

divide into 2 triangles

top triangle: height= 4, base=6

bottom triangle: height= 7, base=6

top=12

bottom=21

Add, 33.

Answer:

B

Step-by-step explanation:

50 +125 = 175 student tickets sold

175x4=$700 from student tickets

50x6=$300 from adult tickets

700+300 = $1000 total made

Answer:

3(4)^2+7(4)(3)-6(3)^2

= 78

A car engine has an efficiency of about 30% is a true statement.

the  factual  effectiveness of a auto machine can vary grounded on  colorful factors  similar as machine size, type, and design, as well as driving conditions and  conservation.   The  effectiveness of an machine is a measure of how  important of the energy produced by the energy is converted into useful work,  similar as turning the  bus of a auto.

In an ideal situation, an machine would convert all the energy from the energy into useful work. still, due to  colorful factors  similar as  disunion and heat loss, this isn't possible.   The  effectiveness of a auto machine is  generally calculated by dividing the  quantum of energy produced by the energy by the  quantum of energy used by the machine. This is known as the boscage  thermal  effectiveness( BTE) of the machine.

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Answer:

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

if you add 1 +1 it will give you 2 but if you add 2+2 it will give you 4

In hypothesis testing, the critical value is a number that establishes the boundary of the rejection region. Option D is the correct answer.

A test statistic is generated in order to decide whether to accept or reject the null hypothesis. The test statistic's numerical value serves as the foundation for the choice. There are in fact two approaches for obtaining at that conclusion; the crucial value approach and the p-value approach

The observed test statistic's extremeness in comparison to a set critical value is assessed by using the critical value technique. As a result, the critical value, or some other form of cutoff value, is compared to the observed test statistic. The null hypothesis is disregarded if the test statistic is more extreme than the crucial value. The null hypothesis cannot be proven if the test statistic does not exceed the critical value in extremes.

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The complete question is, "In hypothesis testing, the critical value is  _____.

a) the same as the p-value

b) the probability of a Type II error

c) the probability of a Type I error

d) a number that establishes the boundary of the rejection region"

In hypothesis testing, the critical value is a threshold used to determine whether to reject or fail to reject the null hypothesis.

In hypothesis testing, the critical value is a threshold that is used to determine whether to reject or fail to reject the null hypothesis. The null hypothesis assumes that there is no significant difference or relationship between variables. The critical value is based on the chosen level of significance, which represents the probability of making a Type I error (rejecting the null hypothesis when it is actually true).

The critical value is obtained from a statistical table or calculated using a statistical software based on the desired level of significance and the degrees of freedom. The degrees of freedom depend on the specific hypothesis test being conducted. The critical value is then compared to the test statistic calculated from the sample data.

If the test statistic is greater than the critical value, it falls in the rejection region, and the null hypothesis is rejected. This means that there is sufficient evidence to support the alternative hypothesis, which suggests a significant difference or relationship between variables. On the other hand, if the test statistic is less than the critical value, it falls in the non-rejection region, and the null hypothesis is not rejected. This means that there is not enough evidence to support the alternative hypothesis.

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The binary expanded form of 19 is 1×2⁴ + 0×2³ + 0×2² +1×2¹ + 1×2⁰

To convert 19 to binary expanded form, we need to convert 19 into a base two number by dividing 19 by 2 and taking into the reminder. Thus:

Dividend   Remainder

19/2 = 9          1      ∧

9/2 = 4           1       |

4/2 = 2          0       |

2/2 = 1           0       |

1/2 = 0            1       |

Then we will write the remainder from bottom to top following the direction of the arrow. Thus, 19 in base 2 is:

19₁₀ = 10011₂

To write binary expanded form, multiply the binary number obtained by 2 and raise them to a power starting from 0 by counting from the right. That is:

19₁₀ = 1×2⁴ + 0×2³ + 0×2² +1×2¹ + 1×2⁰

Therefore, 19 in binary expanded form is 1×2⁴ + 0×2³ + 0×2² +1×2¹ + 1×2⁰

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The mathematicians credited with developing the mathematical models that predict population growth in each of two competing species are Rosenzweig and MacArthur(OPTION A).

These two scientists developed a theory known as the "competitive exclusion principle," which states that two species competing for the same resources cannot coexist indefinitely. Instead, one species will eventually outcompete and displace the other species.
Rosenzweig and MacArthur's model is based on the Lotka-Volterra equations, which are a set of differential equations that describe the dynamics of predator-prey relationships. They extended this model to include two competing species and developed the concept of the "ecological niche" – the specific set of environmental conditions under which a species can survive and reproduce.
Their model predicts that the two species will reach a stable equilibrium, where their populations remain relatively constant over time. However, the exact outcome of the competition depends on several factors, including the initial population sizes of the two species, the relative strengths of their ecological niches, and the availability of resources.
Overall, Rosenzweig and MacArthur's mathematical model has been influential in the field of ecology, providing a framework for understanding how competing species interact and how ecosystems evolve over time.

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\(\qquad\qquad\huge\underline{\boxed{\sf Answer}}\)

Let's evaluate ~

\(\qquad \sf  \dashrightarrow \: \dfrac{1}{3 {}^{ - 2} \times {x}^{ - 4} \times {y}^{2} } \)

plug in the values :

\(\qquad \sf  \dashrightarrow \: \dfrac{1}{3 {}^{ - 2} \times {3}^{ - 4} \times { - 1}^{2} } \)

\(\qquad \sf  \dashrightarrow \: \dfrac{1}{3 {}^{ - 6} {}^{ } {}^{} } \)

\(\qquad \sf  \dashrightarrow \: {3}^{6} \)

\(\qquad \sf  \dashrightarrow \:729\)

Therefore, B is the Correct choice ~

・ ．━━━━━━━†━━━━━━━━━．・

Answer:

729

Step-by-step explanation:

Given expression:

\(\sf \dfrac{1}{3^{-2}x^{-4}y^2}\)

Apply exponent rule \(\sf \dfrac{1}{a^{-b}}=a^b\)

\(\sf \implies \dfrac{3^2x^4}{y^2}\)

\(\sf \implies \dfrac{9x^4}{y^2}\)

Substituting x = 3 and y = -1:

\(\sf \implies \dfrac{9(3)^4}{(-1)^2}\)

\(\sf \implies \dfrac{9 \cdot 81}1}\)

\(\sf \implies 729\)

Based on the given angles, the missing answers of the sequences uploaded screenshots are:

The following answers are constructed based on the sequences of each problems not as the sequences of the uploaded screenshots.

3. Since ∠1 + ∠2 = 180°; then both are supplementary angles

4. Both ∠1 and ∠2 have equal size of angle and share no adjacent side; then both are vertical angles

5. 116° + 64° = 180°; then both are supplementary angle

8. Angles ∠3 and ∠4 are adjacent supplementary because it shares an adjacent side and its sum is 180°.

10. Angles ∠3 and ∠5 are vertical since they share no adjacent side but have equals size of angle.

12. Angles ∠1 and ∠5 are adjacent but neither complementary or supplementary because it sums are not 90° either 180°.

13. x and 107° are vertical angles; then:

x = 107°

15. x and 142° are supplementary angles; then:

x + 142° = 180°

x = 38°

17. ∠RST = 112°

∠RST = x + 87° = 112°

x = 35°

19. It is given that:

x + 127 = 180°

x = 53°

x = y = 53°

y + z = 90°

53° + z = 90°

z = 37°

21. ∠G + ∠H = 180°

51° + ∠H = 180°

∠H = 129°

22. ∠1 = ∠2

∠2 = 128°

23. ∠J + ∠K = 90°

∠J + 73° = 90°

∠J = 17°

2. Corresponding angles and congruent

4. Alternate interior angles and congruent

6. Consecutive interior angles and supplementary

8. Alternate exterior angles and congruent

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Answer:

Add 3 each time. (for question #8)

Step-by-step explanation:

9+3=12

12+3=15

15+3=18

18+3=21

21+3=24

24+3=27

.

.

.

Answer:

The answer is ≈3 to the nearest whole number

Step-by-step explanation:

using SOH CAH TOA

BCA

sin0=opp/hyp

sin0=7.9/11

0=sin‐¹(7.9/11)

0=46 to the nearest degree

<A=<D

so,<EDF=46°

tan0=adj/hyp

tan46=x/3.3

x=tan46×3.3

x=3 to the nearest whole number

Answer:

1/72

Step-by-step explanation:

Probability of getting a 4 on white cube is:

P(W) · P(4) = 1/2 × 1/6 = 1/12

P(R) · P(>4) = 1/2 × 2/6 = 1/6

multiply both probabilities:  1/12 × 1/6 = 1/72

The error is that vertical angles are congruent, and don't necessarily add to 180°. Vertical angles only add to 180° if they are right angles.

\(13x+45+19x+3=180 \\ \\ 32x+48=180 \\ \\ 32x=132 \\ \\ x=33/8\)

Answer:

x = 7

Step-by-step explanation:

Vertical Angle Theorem

When two straight lines intersect, they form two pairs of angles.  The vertically opposite (non-adjacent) angles are congruent.

Angles on a Straight Line Theorem

The sum of angles formed on a straight line is equal to 180°.

The error made is confusing the Vertical Angle Theorem with the Angles on a Straight Line Theorem.  To find x, we should either:

Applying the Vertical Angle Theorem:

\(\boxed{\begin{aligned} (13x+45)^{\circ} &=(19x+3)^{\circ} \\13x+45&=19x+3\\13x+42&=19x\\42&=6x\\x&=7\end{aligned}}\)

Applying the Angles on a Straight Line Theorem:

\(\boxed{\begin{aligned}(6x+2)^{\circ}+(19x+3)^{\circ}&=180^{\circ}\\6x+2+19x+3&=180\\25x+5&=180\\25x&=175\\x&=7\end{aligned}}\)

Therefore, the value of x is \(\boxed{x=7}\) .

To show that the general term of the quadratic number pattern is given by \(tn = n^2 + 4n - 12\) , we need to find a quadratic expression that fits the given pattern.

Let's examine the given sequence: -7, 0, 9, 20. We notice that each term is increasing by a certain amount.

First, let's find the differences between consecutive terms:
0 - (-7) = 7
9 - 0 = 9
20 - 9 = 11

We observe that the differences between consecutive terms are not constant, so this indicates that the sequence is not linear.

To determine if the sequence follows a quadratic pattern, let's find the second differences:
9 - 7 = 2
11 - 9 = 2

The second differences are constant, which suggests a quadratic pattern.

Now, let's find the quadratic expression. We know that the general term of a quadratic sequence can be written as \(tn = an^2 + bn + c\), where a, b, and c are constants to be determined.

Using the given terms, we can form three equations:

1.\(For n = 1: -7 = a(1)^2 + b(1) + c\)
2. \(For n = 2: 0 = a(2)^2 + b(2) + c\)
3.\(For n = 3: 9 = a(3)^2 + b(3) + c\)

Simplifying these equations, we get:
1. a + b + c = -7
2. 4a + 2b + c = 0
3. 9a + 3b + c = 9

Solving this system of equations, we find a = 1, b = 4, and c = -12.

Therefore, the general term of the quadratic number pattern is given by\(tn = n^2 + 4n - 12\).

The general term of the quadratic number pattern is \(tn = n^2 + 4n - 12\).

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The probability of the trainer choosing all the girls first or a boy is 1, or 100%.

To find the likelihood of occasion An or B, we really want to add the probabilities of the singular occasions An and B, and afterward deduct the likelihood of their convergence (the situation where the two occasions happen).

The likelihood of occasion A (picking the two young ladies) is 1/3, since there is just a single gathering with the two young ladies out of three potential gatherings.

The likelihood of occasion B (picking a kid first) is 2/3, since there are two gatherings with a kid as the principal player out of three potential gatherings.

The likelihood of their convergence (picking the two young ladies and having the main player be a kid) is 0, since it is difficult to have the two occasions happen all the while.

Consequently, P(A or B) = P(A) + P(B) - P(A and B) = 1/3 + 2/3 - 0 = 1.

The likelihood of the mentor picking every one of the young ladies first or a kid is 1, or 100 percent. This is on the grounds that the main other chance (picking the two young ladies and having the primary player be a kid) is inconceivable, so either occasion An or occasion B should happen.

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The probability of a passengers waiting at the stop less than 5 minutes and more than 10 minutes is equal to 1/6 and 2/3 respectively.

Probability that the passenger waits less than 5 minutes for the train,

Area under the probability density function (PDF) of the arrival time distribution from 7:00am to 7:05am.

Distribution is uniform,

PDF is a constant function over the interval [7:00am, 7:30am] .

With height 1 / (30 minutes - 0 minutes) = 1/30.

Area under the PDF from 7:00am to 7:05am is,

Probability of waiting less than 5 minutes

= area under PDF from 7:00am to 7:05am

= (1/30) ×(5 - 0) minutes

= 1/6

Probability that the passenger waits less than 5 minutes for the train is 1/6.

Probability that the passenger waits more than 10 minutes for the train is

= Area under the PDF from 7:00am to 7:30am -  area under the PDF from 7:00am to 7:10am.

Area under PDF from 7:00am to 7:30am

= (1/30) × (30 - 0) minutes

= 1

Area under PDF from 7:00am to 7:10am

= (1/30) × (10 - 0) minutes

= 1/3

Area under PDF from 7:10am to 7:30am

= 1 - 1/3

= 2/3

Probability of waiting more than 10 minutes

= area under PDF from 7:10am to 7:30am

= (1/30) × (30 - 10) minutes

= 2/3

Probability that the passenger waits more than 10 minutes for the train is 2/3.

Therefore, the probability of waiting less than 5 minutes and waiting more than 10 minutes is equal to 1/6 and 2/3 respectively.

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The value is approximately equal to 12.0711°

While measuring angles, we use various units of measurements such as the degrees or the SI unit radians as per our convenience.

When we use the degree system, we can use the degree-minute-second or the degree decimal system as per our requirement of precision.

The angle in degree - minutes - seconds is 12°4'16"

We know that \(\frac{1}{60}\) of a degree is minute and \(\frac{1}{60}\) of a minute is a second.

Hence, \(\frac{1}{3600}\) of a degree is a second.

Therefore the angle \(\theta\) in degrees and decimal fractions of degrees will be:

\(\theta\) = \(12+\frac{1}{60}\) × 4 + \(\frac{1}{3600}\) × 16

 = \((12+\frac{1}{15}+\frac{1}{225} )\)°

The value is approximately equal to 12.0711°

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The given question is incomplete, complete question is:

The angle 12 degrees 4'16" is given in degrees, arcminutes, and arcseconds. How do you rewrite them in degrees and decimal fractions of degrees?

The relative frequency of a student being a tenth grader that gets their news from the internet is 0.79.

What is frequency ?

Frequency refers to the number of times that an event or value occurs within a specific period or dataset. It is a measure of how often a particular value or category appears in a set of data. The frequency can be expressed as an absolute count or as a proportion or percentage relative to the total number of observations in the dataset. Frequency is often used in statistical analysis to describe the distribution of data and to calculate various measures of central tendency and variability.

The relative frequency of a student being a tenth grader that gets their news from the internet is given by:

(number of tenth graders who get their news from the internet) / (total number of students)

So, the relative frequency for tenth graders is

34/175 = 0.194

Rounding to the nearest hundredth gives 0.19.

Therefore, the relative frequency of a student being a tenth grader that gets their news from the internet is 0.79.

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Answer:

\( Total \:area\approx 290.5\: ft^2 \)

Step-by-step explanation:

Total area \( =\frac {1}{2} \pi r_1^2 +\frac {1}{2} \pi r_2^2 \)

(where \( r_1 = 22/2 = 11 \: ft, \: \:\:r_2 = (30-22)/2 = 4 \: ft\))

\(\therefore Total \:area=\frac {1}{2} \pi( r_1^2 + r_2^2) \)

\(\therefore Total \:area=\frac {1}{2} \times 3.14(11^2 + 8^2) \)

\(\therefore Total \:area=1.57(121 + 64) \)

\(\therefore Total \:area=1.57(185) \)

\(\therefore Total \:area=290.45\: ft^2 \)

\(\therefore Total \:area\approx 290.5\: ft^2 \)