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2 years ago

Determine the maximum number of zeros. Then, determine the x-intercepts of the function. x^3-3x^2-22x+24

Mathematics

1 answer:

JulijaS [17]2 years ago

6 0

Answer:

Three zeros $x=-4,\ x=1,\ x=6$

x-intercepts: (-4,0), (1,0), (6,0)

Step-by-step explanation:

Plot the graph of the function $y=x^3-3x^2-22x+24$ on the coordinate plane. This graph intersects the x-axis at three different points (see attached diagram):

(-4,0);
(1,0);
(6,0).

This means $x=-4,\ x=1,\ x=6$ are zeros of the function $y=x^3-3x^2-22x+24$

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A toy manufacturer wants to know how many new toys children buy each year. A sample of 601 children was taken to study their pur

Lilit [14]

Answer:

The confidence interval is 6.6<μ<6.8.

Step-by-step explanation:

We have:

Number of observations = 601

Mean = 6.7

Standard deviation σ = 1.5

The z-score for a 95% confidence interval is 1.96.

The limits of the confidence interval can be calculated as

$X \pm z*\frac{\sigma}{\sqrt{n}}\\\\LL=X-z*\frac{\sigma}{\sqrt{n}}=6.7-1.96*\frac{1.5}{\sqrt{601} } =6.7-0.1199=6.6\\\\UL=X+z*\frac{\sigma}{\sqrt{n}}=6.7+1.96*\frac{1.5}{\sqrt{601} } =6.7+0.1199=6.8$

The confidence interval is 6.6<μ<6.8.

7 0

2 years ago

Two geometrically similar jugs have volumes of 1000 cm3and 512 cm3.They have circular bases. The diameter of the base of the lar

Aleks [24]

Complete Question

Two geometrically similar jugs have volumes of 1000 cm³and 512 cm³.They have circular bases. The diameter of the base of the larger jug is 9 cm.

Calculate the diameter of the smaller jug.

Answer:

7.2 cm

Step-by-step explanation:

To solve the above question,we have the proportion

Smaller volume/ Larger volume = (Smaller diameter/ Larger diameter)³

We are to find the smaller diameter

Hence our formula is give as

Cube root(Smaller volume/ Larger volume)= Smaller diameter/ Larger diameter

=cube root( 512/1000) = x/9

= 8/10 = x/9

Cross Multiply

10x = 8 × 9

10x = 72

x = 72/10

x = 7.2cm

Therefore, the diameter of the second jug is 7.2 cm

3 0

2 years ago

Really need help with this .

lions [1.4K]

Answer:

Step-by-step explanation:

The attached photo shows the diagram of quadrilateral QRST with more illustrations.

Line RT divides the quadrilateral into 2 congruent triangles QRT and SRT. The sum of the angles in each triangle is 180 degrees(98 + 50 + 32)

The area of the quadrilateral = 2 × area of triangle QRT = 2 × area of triangle SRT

Using sine rule,

q/SinQ = t/SinT = r/SinR

24/sin98 = QT/sin50

QT = r = sin50 × 24.24 = 18.57

Also

24/sin98 = QR/sin32

QR = t = sin32 × 24.24 = 12.84

Let us find area of triangle QRT

Area of a triangle

= 1/2 abSinC = 1/2 rtSinQ

Area of triangle QRT

= 1/2 × 18.57 × 12.84Sin98

= 118.06

Therefore, area of quadrilateral QRST = 2 × 118.06 = 236.12

6 0

2 years ago

Read 2 more answers

How much is 11+5+3x2+8x1?

adoni [48]

11+5=16 3x2= 6 8x1= 8 so add it together, 16 + 6 + 8 = 30.

8 0

2 years ago

Read 2 more answers

3x+9y=75<br>8x+5y=67 <br>what is x and y?

slava [35]

There are many ways to solve simultaneous linear equations. One of my favorite for finding integer solutions is graphing. The attached graph shows the solution to be ...

... (x, y) = (4, 7)

_____

You can also use Cramer's Rule, or the Vedic math variation of it, which tells you the solution to

$ax+by=c\\dx+ey=f$

is given by

$x=\dfrac{bf-ec}{\Delta}\\\\y=\dfrac{cd-fa}{\Delta}\qquad\text{where $\Delta=bd-ea$}$

Here, that means

... x = (9·67-5·75)/(9·8-5·3) = 228/57 = 4

... y = (75·8-67·3)/57 = 399/57 = 7

_____

A (graphing) calculator greatly facilitates either of these approaches.

8 0

2 years ago