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2 years ago

If A = w + 9 and B = w - 3, find an expression that equals 3A - B in standard form. Please help very urgent!!

Mathematics

1 answer:

Scorpion4ik [409]2 years ago

3 0

Answer:

2w + 30

Step-by-step explanation:

If A = w + 9, B = w - 3

3A - B

3 ( w + 9 ) - ( w - 3 )

= 3w + 27 - w + 3

= 2w + 30

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Anna’s bank gives her a loan with a stated interest rate of 10.22%. How much greater will Anna’s effective interest rate be if t

nata0808 [166]

If the interest rate is compounded daily, we have the effective interest rate calculated as:
r = (1 + 0.1022/30)^30 -1
r = 0.1074 or 10.74%

Therefore, the effective interest rate if the compounded daily rather than monthly is 10.74-10.22 = 0.52 points higher.

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2 years ago

Complete the square to rewrite y = x2 - 6x + 15 in vertex form. Then state

love history [14]

Since $x^2$ is the square of x and 6x is twice the product between x and 3, the second square must be 3 squared, i.e. 9.

So, if we think of 15 as 9+6, we have

$x^2-6x+9+6 = (x-3)^2+6$

Which is the required vertex form. This form tells us imediately that the vertex is the point (3,6).

Since the leading coefficient is 1, the parabola is facing upwards (it's U shaped), so the vertex is a minimum.

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2 years ago

A researcher evaluates the significance of a multiple-regression equation and obtains an F-ratio with df = 2,24. How many partic

alisha [4.7K]

Answer:

N=27 participants

Step-by-step explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

When we conduct a multiple regression we want to know about the relationship between several independent or predictor variables and a dependent or criterion variable.

If we assume that we have $k$ independent variables and we have $j=1,\dots,j$ individuals, we can define the following formulas of variation:

$SS_{total}=\sum_{j=1}^n (y_j-\bar y)^2$

$SS_{regression}=SS_{model}=\sum_{j=1}^n (\hat y_{j}-\bar y)^2$

$SS_{error}=\sum_{j=1}^n (y_{j}-\hat y_j)^2$

And we have this property

$SST=SS_{regression}+SS_{error}$

The degrees of freedom for the model on this case is given by $df_{model}=df_{regression}=k=2$ where k =2 represent the number of variables.

The degrees of freedom for the error on this case is given by $df_{error}=N-k-1=24$ . Sinc we know k we can find N.

$N=24+k+1=24+2+1=27$

And the total degrees of freedom would be $df=N-1=27 -1 =26$

On this case the correct answer would be N=27 participants

6 0

2 years ago

On Friday there were 8 snowboarders for every 3 skiers at Slovak ski resort. On Saturday the ratio of the number of snowboarders

atroni [7]

Answer:

There are 46 more skiers than snowboarder

Step-by-step explanation:

Given

Ratio of Snowboarders to Skiers

On Friday:

$Ratio = 8 : 3$

On Saturday:

$Ratio = 4 : 7$

Population = 168

Required

Determine the difference in the number of skiers and snowboarders on Saturday

On Saturday, we have

$Ratio = 4 : 7$

Calculate Total

$Total = 4 + 7$

$Total = 11$

Calculate the number of skiers

$Skiers = \frac{7}{11} * 168$

$Skiers = \frac{1176}{11}$

$Skiers = 107$ (Approximated)

Calculate the number of snowboarders

$Snowboarders = \frac{4}{11} * 168$

$Snowboarders = \frac{672}{11}$

$Snowboarders = 61$ (Approximated)

Calculate the difference

$Difference = 107 - 61$

$Difference = 46$

<em>Hence, there are 46 more skiers than snowboarder</em>

6 0

2 years ago

The variable complex number z is given by z=1+cos 2θ+isin2θ,where θ takes all values in the interval −1/2π<θ<1/2π

FinnZ [79.3K]

The given complex number is
z = 1 + cos(2θ) + i sin(2θ), for -1/2π < θ < 1/2π

Part (i)
Let V = the modulus of z.
Then
V² = [1 + cos(2θ)]² + sin²(2θ)
= 1 + 2 cos(2θ) + cos²2θ + sin²2θ

Because sin²x + cos²x = 1, therefore
V² = 2(1 + cos2θ)

Because cos(2x) = 2 cos²x - 1, therefore
V² = 2(1 + 2cos²θ - 1) = 4 cos²θ
Because -1/2π < θ < 1/2π,
V = 2 cosθ PROVEN

Part ii.
1/z = 1/[1 + cos2θ + i sin 2θ]
$\frac{1}{z} = \frac{(1+cos2\theta - i\, sin2\theta)}{(1 + cos 2\theta + i\, sin 2\theta)(1+cos2\theta - i \,sin2\theta)}\\ = \frac{1+cos2\theta - i \,sin 2\theta}{(1+cos2\theta)^{2} + sin^{2}2\theta}$

The denominator is
$(1+cos2\theta)^{2}+sin^{2}2\theta \\ = 1+2cos2\theta+cos^{2}2\theta+sin^{2}2\theta \\ =2cos2\theta+2 \\ = 2(1+cos2\theta)$

Therefore
$\frac{1}{z} = \frac{1}{2} -i \frac{sin2\theta}{2(1+cos2\theta)}$

The real part of 1/ = 1/ (constant).

6 0

2 years ago

If A = w + 9 and B = w - 3, find an expression that equals 3A - B in standard form. Please help very urgent!!​

If A = w + 9 and B = w - 3, find an expression that equals 3A - B in standard form. Please help very urgent!!