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Arturiano [62]
2 years ago
14

Dana is buying Grandparents' Day gifts at the mall. She spends $13.75 on a teacup for her grandmother. She spends 4/5 of that on

a coffee mug for her grandfather. How much money does Dana spend in all?
Mathematics
1 answer:
marysya [2.9K]2 years ago
7 0

The total money Dana spent in all is $24.75

<h3>Ratio and proportions</h3>

Ratio are written as fractions of two integers. For instance a/b.

Amount spent for grandmother = $13.75

Amount spent on grand father = 4/5 * 13.75

Amount spent on grand father = $11

Take the sum

Total money spent = $13.75 + $11

Total money spent = $24.75

Hence the total money Dana spent in all is $24.75

Learn more on proportion here: brainly.com/question/19994681

#SPJ1

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Determine if each of the following sets is a subspace of Pn, for an appropriate value of n.
snow_tiger [21]

Answer:

1) W₁ is a subspace of Pₙ (R)

2) W₂ is not a subspace of Pₙ (R)

4) W₃ is a subspace of Pₙ (R)

Step-by-step explanation:

Given that;

1.Let W₁ be the set of all polynomials of the form p(t) = at², where a is in R

2.Let W₂ be the set of all polynomials of the form p(t) = t² + a, where a is in R

3.Let W₃ be the set of all polynomials of the form p(t) = at² + at, where a is in R

so

1)

let W₁ = { at² ║ a∈ R }

let ∝ = a₁t² and β = a₂t²  ∈W₁

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t²) + c₂(a₂t²)

= c₁a₁t² + c²a₂t²

= (c₁a₁ + c²a₂)t² ∈ W₁

Therefore c₁∝ + c₂β ∈ W₁ for all ∝, β ∈ W₁  and scalars c₁, c₂

Thus, W₁ is a subspace of Pₙ (R)

2)

let W₂ = { t² + a ║ a∈ R }

the zero polynomial 0t² + 0 ∉ W₂

because the coefficient of t² is 0 but not 1

Thus W₂ is not a subspace of Pₙ (R)

3)

let W₃ = { at² + a ║ a∈ R }

let ∝ = a₁t² +a₁t  and β = a₂t² + a₂t ∈ W₃

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t² +a₁t) + c₂(a₂t² + a₂t)

= c₁a₁t² +c₁a₁t + c₂a₂t² + c₂a₂t

= (c₁a₁ +c₂a₂)t² + (c₁a₁t + c₂a₂)t ∈ W₃

Therefore c₁∝ + c₂β ∈ W₃ for all ∝, β ∈ W₃ and scalars c₁, c₂

Thus, W₃ is a subspace of Pₙ (R)

8 0
3 years ago
Equation for dividing example 25 divided by 5
Dafna11 [192]

Answer: Example: 15 ÷ 5

Step-by-step explanation:

6 0
3 years ago
In an experiment you do a chi-square test comparing observed and expected progeny. Your calculated chi square is 0.375. With 1 d
myrzilka [38]

Answer:

It mean that the observed progeny is similar than the expected progeny. There is no a relationship between the categorical variables.

Step-by-step explanation:

The Chi-squared test is used to test the relationship between categorical variables. A categorical variable is a non-numerical variable. The null hypothesis of the Chi-squared test is that categorical variables are independent; it means that the frequencies are not dependent on the variable. It is important to know that the Chi-squared test does not measure causality, it only measures the relationship. To reject the null hypothesis, you usually need a probability lower than 0.05, but in this case, the probability was way higher than 0.05, it was between 0.5 and 0.9.

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3 years ago
Last Tuesday was silly hat day at Toby's school. 74 students wore a silly hat and 666 students did not. What percentage of the s
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Answer:

10%

Step-by-step explanation:

The total population of students will be equal to the sum of both those who wore the silly hat and those who didn't hence

Total students= 74+666=740

Number of students who wore silly hat is given as 74 hence when expressed as a percentage of the total students' population we get that

percentage of the students wore a silly hat=\frac {74\times 100}{740}=10\%

Therefore, 10% of students wore a silly hat last Tuesday

4 0
3 years ago
Use a property of equality to solve this equation 4.5x=18
algol13

Answer:

x=4

Step-by-step explanation:

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