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3 years ago

Find the length of the shorter diagonal of a rhombus if:

Mathematics

1 answer:

Fudgin [204]3 years ago

8 0

a) Area of rhombus = ½ * (diagonal1)*(diagonal 2)

Let diagonal (D2 )= longer diagonal = 15 and diagonal (D1) = shorter diagonal

90 = ½ (D1)*15

90 = 7.5 D1

Now divide both side by 7.5

90/7.5 = d1

D1= 12 units.

b) Area of rhombus = ½ * (diagonal1)*(diagonal 2)

Let the ratio be $x$

Diagonal 1= $2x$

Diagonal 2= $3x$

147 = ½ * $(2x)*(3x)$

Multiply both side by 2

294 = $(2x)*(3x)$

294 = 6 $x^2$

Divide both side by 6

294/6 = 6 $x^2$ /6

49 = $x^2$

$x$ = 7 unit

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Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a rand

SOVA2 [1]

Answer:

Question 1:

(a) P(x<60) = 0.9236

(b) P(x>16) = 0.9564

(c) P(16<x<60) = 0.88

(d) P (x>60) = 0.0764

Question 2:

(a) P(x<3) = 0.0668

(b) P(x>7) = 0.0062

(c) P(3<x<7) = 0.927

Step-by-step explanation:

Question 1:

x = no. of mg of porphyrin per deciliter of blood.

μ = 40

σ = 14

(a) We need to compute P(x<60). We need to find the z-score using the normal distribution formula:

z = (x - μ)/σ

P(x<60) = P((x - μ)/σ < (60 - 40)/14)

= P(z < 20/14)

= P(z<1.43)

Using the normal distribution probability table we can find the value of p at z=1.43.

P(z<1.43) = 0.9236

so, P(x<60) = 0.9236

(b) P(x>16) = P(z>(16-40)/14)

= P(z>-1.71)

= 1 - P(z<-1.71)

= 1 - 0.0436

P(x>16) = 0.9564

(c) P(16<x<60) = P((16-40)/14) < x < (60-40)/14)

= P(-1.71 < z < 1.43)

This probability can be calculated as: P(z<1.43) - P(z<-1.71)

P(16<x<60) = 0.9236 - 0.0436

P(16<x<60) = 0.88

(d) P(x>60) = 1 - P(x<60)

we have calculated P(x<60) in part (a) so,

P(x>60) = 1 - 0.9236

P (x>60) = 0.0764

Question 2:

μ = 4.5 mm

σ = 1.0 mm

In this question, we will again compute the z-scores and then find the probability from the normal distribution table.

(a) P(x<3) = P(z<(3-4.5)/1)

= P(z<-1.5)

P(x<3) = 0.0668

(b) P(x>7) = 1 - P(x<7)

= 1 - P(z<(7-4.5)/1)

= 1 - P(z<2.5)

= 1 - 0.9938

P(x>7) = 0.0062

(c) P(3<x<7) = P(x<7) - P(x<3)

we have computed both of these probabilities in parts (a) and (b) so,

P(3<x<7) = 0.9938 - 0.0668

P(3<x<7) = 0.927

6 0

3 years ago

What number will the function return if the input is 15.4?

wlad13 [49]

The rule of the function is to multiply the input by 3, since one yard is equal in length to three feet.

So, if the input is 15.4, the output will be

$f(x)=3x \implies f(15.4)=3\cdot 15.4 = 46.2$

4 0

3 years ago

Find the ordered pair whose x-coordinate is 5. 4x=6y+8

sukhopar [10]

(6, 2 )

substitute x = 5 into the equation and solve for y

6y + 8 = 20 ( subtract 8 from both sides )

6y = 12 ( divide both sides by 6 )

y = $\frac{12}{6}$ = 2

the ordered pair is (5, 2 )

6 0

3 years ago

Read 2 more answers

Springer was a political candidate running for Congress. He was operating on a tight budget and instructed his campaign staff no

tatuchka [14]

Answer

In the event that a purchase was made for a campaign without it being managed by the staff in charge of this management, with a proposal not to pay because the person who bought it was not this staff but the candidate, the selling company, Dubychek , is in everything correct when alleging the payment, the candidate knew of the situation and it is known that the representative, goes in the name of this candidate.

6 0

3 years ago

Which equation represents the graph shown? (Picture attached)

Maurinko [17]

Answer:

correct answer is option B

Step-by-step explanation:

as we know equation of line

y = m x + c....................(1)

where c is the intercept

m is the slope

m = $\dfrac{y_2-y_1}{x_2-x_1}$

m = $\dfrac{35-0}{1-0}$

m = 35

putting value of m in equation (1)

we get

y = 35 x + c

from the graph we can clearly see that line is passing through (0,0) hence

0 = 35 (0)x + c

c = 0

hence the equation of line comes out to be

y = 35 x

correct answer is option B

8 0

3 years ago